UK is 1st on the moon
POD (end of war in Europe, not end of the year, though): In 1945, Churchill realises better how disgruntled the British soldiers are with his government. Just in time, he manages to turn around his fate with more campaigning among his soldiers. He wins the election and reigns for another term.
While his heavy handed style won't be all successful, at least he will avoid the efforts to turn Britain into a welfare state and other such misguided reforms. He will also bargain slightly harder about Germany, about the colonies, and so on, though India will become independent as IOTL. He will be less inclined to sell out British technology and business interests. More money in arms and infrastructure instead of an extreme bureaucracy and social engineering will instead keep Britain in the race with the US and the SU.
Butterfly1: He realises after 4 years that a few of his tactics did not really make him too popular, but manages to get a conservative successor of his choice into the next term. His successor is weak and loses the next election, but now it's 1953 or so.
By then, the British were able to see the ugly face of real socialism, and Labour also moved towards the political middle due to the long series of election losses. A moderate Labour candidate gets elected and imposes much fewer changes onto the country. The ones that do get through will still be enough to disillusion the British in terms of welfare and socialist ideas. Still, Labour sees full two terms.
Butterfly2: As the Labour Premier happens to be a little on the technocratic side and believes in large government projects, he starts a pretty impressive space program, with an English space port in some British colony close to the equator. This is justified partly to keep bright people from emigrating to the US - thus also putting a minor dent into the American space program. Many scientists from the war ravaged continent are added to the British space program instead of the US one.
In 1961, when the conservatives take over again, the British already shot a man into space, though on something resembling more a rocket plane with boosters than a space capsule. They also managed to put a few short lived satellites into orbit, and tested the feasibility of satellite communications, satellite observation, re-entry from orbit, and so on.
The conservatives decide to move the project more towards a commercial venture, with the goal of spinning off private companies from whatever is successful, while the rest is booked as research. Wheather forecasting, satellite telephony, and so on are invented or copied from the the other 2 space powers and turned into some commercial successes and some commercial failures. The latter are reintegrated into the science part, if they are useful in one way or the other.
All the space activity and other changes in this timeline mean the UK is more successful economically and technologically. This also makes it possible to spend more on space adventures than what's realistic IOTL.
Butterfly3: While the US went the super high-tech, purpose built, all costs allowed way, and the SU tried to realise even the most ambitious ideas with as little cost as possible, but duplicating their efforts, GB goes the middle way - mass producing useful rockets, capsules, and the likes in standard sizes, increasing their sizes only moderately, and using only a conservative amount of untested technology. Double research and the likes is usually avoided.
As automation is not as advanced, and I assume the UK lags slightly behind the US in electronics development, those 1960s style manned satellites are actually put to use by the UK. Small capsules filled with different equipment map the planet, observe wheather, troops, and building activities, provide communications, and so on - in ever increasing flight durations and numbers. GB develops the ability to dock space modules together to form small space stations, mainly to avoid having to haul telescopes, cameras, and other heavy equipment repeatedly into space.
In 1967, GB has all the technologies necessary for a moonlanding. The British assume that both Russians and Americans will land on the moon sometime in that year or a year later, as was tried IOTL, iirc. They attempt to land just a few months later, at the end of 1968, so they start building a landing module and a space booster (the only two parts missing at that time).
Butterfly4: Unlike their competitors, the British are lucky that they are not thrown back in their schedule as much as Russia and maybe the US. They actually manage to land a man on the moon in the middle of 1969, while the US lands in december (a few months later than IOTL due to a few scientists not available to them).
With 2 countries successfully landing on the moon, the SU can't stand behind and actually try to launch their little moon lander - the adventure ending successfully or in a fatality.