Sorry, not 1945. It's interesting, but I simply don't have the knowledge to do it (and I had to spend a lot of time doing research for Primus Inter Pares despite having a decent grasp of the context).
No, we're going to the swinging sixties!
For this TL, would be possible if you wrote out differences in economic policy, and British Society politics, social policy etc, and the world in general.
How so? (geniune question, I didn't get the meaning)
The attitudes in british society, opinions towards different issues.
Economic Policy, what economic policy is in place, and the differance than in RL, nationalised industries, NHS investment etc.
The unemployment rate, scope of social welfare etc.
Social Policy, such as difference to the EU, women's rights, LGBT rights?
The atititudes that are held by the public, presumably more left-wing, and more friendly to the EU.