I think that the overall drop in soft and hard power would be significant, but Britain would have significantly better relations with African and Asian countries if they avoided the Cold War conflicts. It depends, I think, on what East of Suez officially consists of as it could be defined to include the entirety of the Suez Canal, British East Asia, the British presence in the Middle East and sub-Saharan Africa or it could be more strictly defined as just Asia.
That is an interesting point, a withdrawal from East of Suez would allow more of a focus on British holdings West of Suez. The Caribbean in particular seems like a good choice for investment. If Britain has abandoned Asia and Africa, perhaps they invest in the Caribbean territories to rebuild prestige. This could lead to more BOTs or it could lead to Britain further backing the West Indies Federation and the increased support leading it to succeed.
I think you might be on to something here. An earlier British pull-out East of Suez might allow Britain to focus her energies on other territories. I think you might see Britain put more of an effort into integrating Malta into the UK proper (there was a push for this IOTL) and then afterwards Gibraltar. I think you'd likely see Britain retain her Caribbean holdings. They're poor, would greatly benefit from British investment, and have a history of Anglophilia. Perhaps Jamaica, Trinidad & Tobago, and The Bahamas will have parliamentary seats or perhaps they will remain BOTs, I can't say. But I think a strong British presence will be felt in this area of the globe for the time being.
I'm just going to list a few possible idea from this:
1) No Mau Mau Rebellion, if Kenya is barrelling towards independence I imagine the locals may be content to wait and see what happens. Granted my knowledge of the Mau Mau Rebellion extends to GCSE History levels so that could be off. I think and East African Federation was mooted at some point, maybe that's a stopgap solution of some form.
2) Indonesia-Malaysia Confrontation, assuming its not butterflied for whatever reason, would be very different without British forces involved. Its entirely possible Australia could get involved in Britain's stead but I'd say the odds of Indonesia getting North Borneo are much better ITTL.
3) Hong Kong. It wasn't abandoned in the OTL withdrawal East of Suez, frankly it may just be left alone like OTL. I can't imagine the ROC getting it, nor can I imagine it going from Britain to the PRC amiably.
4) Assorted Pacific islands, probably split between US and Australia.
5) Suez Canal, does this go to Egypt earlier, possibly even pre Nasser. A boost in popularity like that could very well cause the Kingdom to survive in some form.
1. Agreed on no Mau Mau rebellion. The British settlers in Central and Southern Africa might move to South Africa if Britain is decolonizing even faster than she did IOTL. This might have interesting effects on South African politics. Perhaps with more white South Africans hailing from Britain, the close Republic referendum of 1960 might go the other way.
2. I think Britain would likely still be involved in the Malaysian Emergency even if she granted that country independence earlier. As for the Konfrontasi, don't see Britain not getting involved either. Britain was in Brunei until 1982. If Indonesia is attacking North Borneo, then British holdings are directly threatened.
3. It will be left alone. Britain has a lease on it and frankly, the PRC wasn't all that interested in getting it back. The reason Deng went hardline for it was because Thatcher made some comment that he thought sullied China's honour and afterwards thought it was a matter of national pride to have it returned. If Thatcher had held her tongue and not made that remark (I don't recall exactly what she said but it's here somewhere on this site) then it'd likely still be British today (if not granted independence).
4. Depends. The Pitcairns will likely remain British. Other than that, I don't think Britain would hand over her territories to the USA; Australia and New Zealand are the more likely beneficiaries (and god knows Britain will need to do some image building in the Antipodes if she pulls out in '48).
5. Agreed. It also gets rid of the Suez Crisis which will do wonders for Anglo-American relations (although they recovered very quickly, the Crisis left deep wounds in Britain's psyche).
I will state, however, that if Attlee does decide to do this, I could see Churchill winning flat out in 1950 rather than leaving Labour with a tiny majority. The move would be seen as a betrayal of Empire and of the Commonwealth. The Tories would be baying for blood.