It would have to rebrand itself somewhat. Empire stuff just doesn’t sound good to Americans and is good propaganda for Soviets.
A commonwealth with uniformed military and economic system is possible. I think the Brits could pull that off with the white dominions at least. It isn’t a empire anymore but more like a EU but scattered across the planet. It’s mutual international cooperation not a empire would have to be depiction of it.
For example, it could be British, Canada, New Zealand, Australia, and South Africa at first. Maybe Caribbean holdings. Ireland could join later in too. Other members could be Rhodesia, Singapore, Hong Kong, or more loyalist former colonies.
Everyone has its own political system domestically and have a British version of EU parliament. All commonwealth also likely retain more ceremonial titles. The bigger and non white ones still likely see empire and never join commonwealth.
The commonwealth could just have stuff like open border, no trade barriers, easy immigration between themselves, and joint defense.
I see the Brits actually liking commonwealth more. Former dominions likely can work with Brits more cordial and mutually then France especially in long run. It also helps solve many problems.
If for example Ireland joined the commonwealth for economic benefits and ties that can be used to ease tensions in Northern Ireland and as propaganda tool against ira. It also can lead to Ireland itself helping more at calming tensions there. If they join commonwealth and if brits are subtle about it which they often are former unionist and loyalist descendants who left Irish republic after independence could move back in republic. Maybe a part of a “good faith” agreement. They are just given duel Irish and British citizenships if they choose too. This makes resettling there easy and tighten trade between two.
Ireland might join because of location and trade with commonwealth members. Most of its more current immigrants are in Canada and British isles. There is also Northern Ireland. They also have people in Australia too. This is more practical and natural move even if they don’t join until EU is around. Ireland likely picks the commonwealth over EU because that would make way more sense.
Africa will be a more grey and unpleasant matter. It does give commonwealth more racial parallels with US. The Anglo Whites in South Africa during 60s at odds with Afrikaans over status of Africans and non whites. Either won’t majority rule but white English speaking South African want a more Rhodesia system over apartheid one. Also not all Africans can causally leave South Africa or Rhodesia yet like whites can. If commonwealth is as big as I describe and has open borders with each other that helps both regimes in Africa gaining more white residents. The Indians, Asians, and mix people often being given equality first.
Letting in skill labor from developing world and former colonies will help them. Immigrants from former colonies that failed can become more pro commonwealth if its doing well. India still gains independence but that does not mean they don’t try to keep more ties with India. I think propping one giant India might help them in long run. India has shown much more willingness to westernized and work with west then Pakistan or even Bangladesh. No Pakistan is one less ally for China and less distractions for India once they stabilize. Maybe US and UK agree to expand Marshall plan to unified greater India as a way to contain communism especially when it starts looking China will go red.
Portugal Empire would have to survive to help them especially in Africa but with full British help and a more passive US they could keep its colonies and actually adopt a more commonwealth type of system like the Brits did once they start to reform and become more democratic. Portugal is also additional help against China over port cities. Portugal would stabilize borders in Africa(less places for partisans or Soviet aid to come from).
During Congo Crisis brits help prop government in Katanga. They can’t keep every colony or prop every failing colonial regime. They have to pick who to help carefully and know when to pull out and hopefully prop up regime made up of former loyalist. One option is Arab/Muslim kingdom off the coast of Tanzania. This becoming like a mix of Dubai and Singapore downline.
They could maybe keep all of Malaysia with Singapore to by playing more favoritisms towards Chinese there. After nationalist start falling in China all brits have to do to make Malaysia majority Chinese is to let many fleeing the communist in as “refugees”(many are but many are not. They just want anti communist Chinese loyal or thankful to them somewhat). Malaysia on mainland and islands already have a native Chinese population that was near majority in many places.
They would be anti communist which helps with getting US on board with it. They would hate communist China. They would not want to live under Muslim rule country and like Hong Kong and Singapore they develop a positive view of brits. Malaysia still given independence but under a Chinese majority government. They also have Singapore and all of former British Malaysia(the Brits screwed Muslims here hard in favor of Chinese there). More Chinese can also move in from Indonesia later on. Malaysia could become a Asian tiger economy and be first Asian majority country to join commonwealth but decades down the line(90s) that isn’t a city state. Hong Kong could be given a special city state status and be part of commonwealth who it is dependent on economically. They are independent with its own government so China invading it or threatening a democratic nation will make them look aggressive and see more international countries turn against them. Hong Kong could be on board with this 100 percent and China Can’t do shit unless they want a war over it which US would be on Hong Kong side.
Suez Crisis going to give UK trouble with Americans. Winning this is a major strategic, political, and symbolic victory but they need to bullshit Americans hard and as long as possible. Hopefully distract or bait them with other world issues or leverage them somehow.
The British controlling Suez is big. They could argue them controlling Suez is similar to Americans in Panama Canal. They would have to give Americans everything they want trade wise to Suez and maybe even give them a base within the Suez Canal Zone. The Soviets are pissed but American agreeing is all they need. France not invading with Brits is preferable here. The British need to come off as least imperialist as possible. The French in all honesty don’t help in that. British should invade with help of Israel. Give them Sinai and take Suez directly. Reinstalled the king if possible. Supporting monarchs would help them. Support kingdoms in Libya and Arab world. This would actually work well with US interest in region. The Brits often did same exact shit as US relating to trade and oil with Muslim world in otl especially gulf region. The shah staying in power as British ally and trade partner is helpful. This indirectly screws China even more in long run because all these conservative pro British/US monarchs might now be able to be rallied together in cutting off or lowering oil trade from China in favor of them.
A schism between US and UK could happen at multiple points but I think it would be way less extreme then Sino Soviet split. More of coming to a point of “conflicting interests or goals” but both still agree on a lot of stuff. The British and commonwealth after recovering from ww2 economically could have its footing again and weathered a lot of post war decolonization era. It would require a lot of luck and skill but not impossible. Propaganda and image are important during Cold War especially with growth of mass but limited media(you had like 6 channels). So brits and commonwealth need to play on that. They already had shared media in otl.
The commonwealth could be British and Anglo Saxon “born again” type of movement after ww2. The time of imperialism has past but “international cooperation and globalization” is way of future. The Brits still bit shaken from war look more away from Europe then otl.
Instead of working with Europe they actually go full on US and overseas(trade with dominions and former empire) after world war 2. The British are helping Americans project and build trade ties within its former empire way more so then otl but at the cost of leaving European affairs almost completely outside of Mediterranean. The French are likely given more of military burden in Europe. They have to cater or appeal to US interests more then European ones.
Suez Crisis shows the British European biases somewhat. They included the French in the invasion plans and goals for Egypt much more so then Americans. That was just straight up dumb on there part. You included a country that you and US liberated a decade ago over unmistakable non communist superpower. Both of your countries also were still getting aid from US to for rebuilding. The Brits might have got way more out of crisis if they included Americans in on it and not French at all. US government isn’t going to trust Brits military wise if they do shit like this. They can’t have anyone questioning their interest and goals within its own bloc especially this early on. Later on brits could push back more especially after Cold War.
The French doing better and retaining more of its empire helps Brits here. The French being forced to cave on its colony in Indochina by US and Brits right after ww2 might upset hell out of them but help them in long run retain more. Basically US, UK, and France(after bitterly agreeing) install a pro western government with many former colonial loyalist. Chinese refugees and immigrants are also let in like Malaysia after it falls to communist(China has plenty of people to have mass migrations from. It’s actually somewhat surprising it was not more common in otl). This is more anti-communist. They could work well with conservative pro western republic in Indochina. This is other place that could get Marshall plan aid. It could also get aid from French and Brits and growing Asian economic tigers around it(China getting surrounded and “contained”. US isn’t going friendly with them like otl because now they got better non communist options). Thailand could hop in on western aid and trade too.
This helps France maintain Algeria and much of its African holdings. The rest are made into pro western puppets. France still goes democratic similar to otl but is much more centralist and a large international military force. The Europeans do have to play ball more and bribe US a good bit if they want to retain any of this in any shape or form. After bitterly giving up Indochina and maybe a few other colonies too they decide it is just pragmatic to work and cater to US. Europeans are used to ruling world or having top say. After ww2 they really don’t have that anymore unless we count Soviets but many of them don’t. They do have to sallow there pride and understand they aren’t always playing from position of power anymore. Good part about US over Soviets is ideology is less important to them. If you can argue a point to them and make it appeal to their desires and interests they will side with you. That’s how capitalism often works. Basically “how does you doing this benefit me”.
France is US shield against USSR and Eastern Front. The first line of defense. They could also be the person keeping African regimes pro western. They install a bunch of francophone puppet states in much of Africa south of Algeria or inland. Algeria and more coastal areas are more directly part of France.
The Europeans need to play it off as nation building, economic cooperation, and “military aid”. This is American world now and during Cold War. Unless you won’t to be communist. They need to copy them and play them at there own game. They can’t do stuff like they use too. Africans who opposed this could be depicted as “communist/socialist” and how “majority” supports our “help” and want to work with us. They show westernized elements of these societies. Some places these they do have majority support but in others not so much. Centralist France could be west way at projecting in Africa and preventing it from going red.
This would appeal to Truman and containment doctrine but the Europeans do have to push and present it to Americans. They do have to play if Americans ignorance and bullshit them. If they see deals as beneficial enough they will agree unless they start losing bad or going to extreme on war crimes but I think France and Brits could know when to hold back. Honestly they might understand that better in long run then Americans later on in this pod.
Making remaining bits of Congo failed state or similar to otl while much of Africa is few settler regimes, pro western puppets, direct positions(not colonies at least in name), and conservative monarchs but all steadily developing nations might discredit many nationalist and anti western elements in Africa. The Marshall plan might be extended to parts of Africa(much later or a “renewed” Marshall plan in 80s). Reagan sends money, guns, and foreign aid to French African puppets like he would send “aid” to Latin America.
A more stable and overall less anti Western Africa does help British/commonwealth retain much more of its own influence there. Bringing in Asians on exploiting of Africa could help them too.
Maybe after Katanga gains it’s independence it we see it join commonwealth later and see Commonwealth use mass Chinese diaspora population to send people there. Instead of a bunch of Chinese dying or getting stuck in communist China they do have somewhat of open door policy towards Chinese people but do direct them to certain places to settle. This actually helps their image among many Chinese people outside of China. These Chinese people would also be much more conservative especially regarding women leading to many having high birth rates especially as economic situation improves. Same goes for Indians too. They could have a more open door immigration policy with Indians too.
Edit: The Americans would likely lower trade and travel barriers between them and a possible commonwealth. Almost all of commonwealth especially at first would be English speaking and white dominated. Later on it be mostly first world or top tier second world countries(South Africa still likely has crime and poverty issues. AIDS could still happen too). Also Canada and Caribbean being part of commonwealth and right next to them would make this a no brainer. It makes tourism industry in Caribbean take off even more. Canada provides economic bond that ties US to commonwealth therefore also becoming even more friendly with UK and commonwealth. China also loses out on trade with Canada since UK and US corner market there more.