A big challenge! (Aren't they a superpower now? They have Trident don't they?)
Seriously. Need to
1. Keep the Empire together and make it stronger - United Kingdom on its own is just too weak.
2. Keep other powers - superpowers in this timeline (US, USSR) or alternate timeline (Germany) from dominating the world
(I use "You" and "We" to indicate the British leadership from now on)
1. This will have to be some kind of federal deal. Particularly involving India - if you are happy to use force maybe it is possible to keep India as a pure subordinate colony, just keeping the army and landowners happy, as long as you don't get into a war you look like losing. But such an India is not a source of strength. So you have to make the Indian population literate, develop industry and still keep them part of the Empire and happy about it(and stop Pakistan splitting off while you were at it). Nehru might have gone for this - he was both philo-British and pro industrialisation. A very tricky political act. But we are just making stuff up, right? Imagine India as part of a federal Empire and industrialised to even Japan's level. An Indian Army equipped from purely Indian sources, at least for the basics. The home islands mainly a shipyard and source of the more sophisticated weapons (at least for the first few decades, if we are imagining more rapid industrialisation then they could be caught up to UK in absolute abilities by now). This would allow both a continental size army and the already good navy and air force. Maybe in the long run you could even do what Adam Smith suggested with the North American colonies and move the capital of the Empire (Commonwealth?) to India, just keeping GBR as a useful naval base (like a big Gibraltar).
Same kind of deal for the white dominions - Canada, Australia, S Af. Maybe Canada is too close to the US, and they all have their own interests. But SAF mostly stayed loyal in WW1. Australia only started acting independent in WW2 once the Japanese looked really threatening. And I am Australian, but frankly, if things work out to plan in India you only need the other colonies to sell you food and fiber. Also, this strategy positively encourages industrialisation in the dominions which would remove one source of friction.
Hanging on to Africa, Burma and Malaya (mainly for raw materials) shouldn't be too hard after everything else I've assumed. Just don't get into a war with Japan and another great power at the same time. (This gets easier and easier the more I write!)
If this is done successfully, it would take an absolute catastrophe for the British Empire to not be a superpower today. Remember Gandhi only got disillusioned with the Empire after he helped the war effort in WW1 and didn't get much back. So it's theoretically possible if you start early.
But let's say it doesn't work. Either India gets independent as in real life, or stays in the Empire but as a weak or hostile colony, not a willing partner.
2a. Niall Ferguson would say, Stay out of WW1. Then Germany wins, France is weakened, and the Germans get the western Russian Empire (Belarus, Poland, Ukraine, Baltics) like at Brest Litovsk. Maybe give this super-Second Reich some of Africa to keep them happy. (Naturally offer French and Belgian colonies before British ones.) Perhaps this could co exist with British India and the white dominions on a long term basis - it's not Hitler we're talking about. Maybe the Russians want to have a go at India to compensate, but if they just got whipped by Germany they're pretty weak. However if India is not going according to 1. and Russia gets its act together within the next century (whether under Communists or something else), this plan is pretty much stuffed. We have to hope they spend all their energy constantly fighting Germany or having civil wars (and maybe help that along a bit).
Another big problem: no carve up of the Ottoman Empire, no Middle East oil. Optimistically, if Britain doesn't fight Germany, Turkey does not come in on Germany's side. But Germany is still friendly with Turkey and won't want Britain hacking off the Arabic provinces like already happened in Egypt. Maybe compensate in Persia, and try to keep on good terms with Germany and Turkey (easier if Russia is your potential enemy) to keep access to Iraq.
Further down the line we face potential troubles with the US and/or Japan. Let's run this like in real life, ditching the Japanese alliance to keep friendly with the US. Japan could be dealt with assuming things come one at a time. Still this is a hard choice. If Japan still wants to expand in China, they will get in trouble with the US, the US will cut off oil, and Japan will move south. Maybe say to Japan (secretly to keep the US happy): Take the Dutch East Indies and we won't fight you. And say to US secretly: We will only fight the Japanese if you do. Again assuming a single front war, should be OK either way. (Of course if we are using perfect hindsight maybe there is some way to mitigate or avoid the Depression and get a less militaristic govt in Japan. But this violates minimal rewrite.)
The ultimate problem is: no Hitler, no official anti-Semitism in Germany, Germany keeps all its scientists. Germany creates the A-bomb way ahead of everyone else and rules the world. Oops.
Both of these had the earliest possible POD - 1914. (Maybe if we stretch it 1. is viable for a few more years, up to Amritsar in 1919.) Now let's assume WW1 went as it did and go later. (I think everyone would admit WW2 as it happened is the point of no return.)
2b Stomp on Hitler early - Rhineland or Sudeten crisis. USA doesn't get dragged in, Japan if she attacks does it on her own (see 2a). Empire stays together longer, USA takes less of a world role. If we accept that Stalin was basically cautious ("socialism in one country") and his successors still more so, the USSR is still powerful but maybe not so much as to leave Britain second rate.
2c Don't guarantee Poland. Let Germany and the USSR fight each other first and then pick up the pieces. (This has been done before; I forget who by.) This could easily turn into Stalin letting Germany fight France and Britain and then picking up the pieces, or the winner of Stalin and Hitler being so strong noone else could touch them. But Hitler thought that France and Britain would fold in 39, so he didn't want to fight them right away, and they would be more ready for war the more time passed.
All four of these are risky but not completely impossible - think of Hitler beating France so fast in 1940, or Lenin seizing power in 1917, say. Or even how Britain got so big an empire in the first place. If we have dictatorial control of the British leadership and hindsight, that is. The problem is that it violates so many attitudes held at the time - reluctance to spend on armaments, or to see Indians as fully equal, or to encourage the Empire to industrialise at the cost of British trade.
What does everyone think?