for the purposes of the discussion, can we assume they can and have.
Will the British Steel industry still nationalized? If not what kind of effects would this have? How would it have effected the United Kingdom's nuclear weapons program?
The Iron & Steel Act was passed in 1949. By the time the Conservatives came into power in October 1951, the Iron & Steel Corporation only existed on paper and no real changes had been made to industry which allowed for symbolic and painless denationalisation. Apart from saving the Civil Service on paperwork, a 1950 Churchill government doesn't change that.
On atomic weapons, the British Government was well on the way to developing a bomb by late 1952, which it did IOTL. Despite Truman being keen to cooperate with Britain following the detonation of Joe-1, the Atomic Energy Commission, fueled by Red Scare, were convinced the Labour ministry couldn't be trusted. Churchill in Number 10 would overturn this, and Winnie's love of America would only help this. So Britain might get the bomb in late 1950 or early 1951 but it would be American built, as was the British hope, supplying expertise in return for American manufacture. It would be interesting to see if Bevan, who by the late 1950s was pro an independent nuclear deterrent, might approve of this earlier, which rob the CND of its premier spokesman. Also if Suez still takes place (I can't see why not), American pressure might antagonise an 'atomic nationalism', as combined with Krushchev's threats of nuclear attack on London, the idea of the United States not being on page with Britain will become patently obvious. It would be interesting to see one of those not-so rare alliances of the Hard Left and Conservative Imperialists in the mid 1950s particularly as Gaitskell was quite pro-American.
Ultimately I see Britain developing her own atomic arm later if political realities demand it (given the period and British politics in general I doubt it), which might save some of the scrapped bomber plans. However I don't see Britain taking a particularly stronger anti-American stance in the long run, though Washington's 'betrayal' might have longer legs in some quarters (who knows how it might effect Enoch Powell's trajectory).