It's true that the UK was a major recipient of Marshall Plan funds, and like elsewhere in Western Europe, these funds helped the UK pull out of the economic devastation of war and 'balance its budget'—a budget in which the health service was part. It's also true that the NHS was an expensive venture, and that the staggering demand for services upon launch drove up the costs beyond what its planners anticipated. This surge in demand was perceived by many policymakers as a major drain on a fragile postwar economy. (A perception that may not have been entirely accurate-- see my earlier post on the early financing of the NHS.)

But the NHS was not ever contingent on the Marshall Plan. The timeline is the clearest evidence of this: the law creating the NHS, the National Health Service Act, was passed in 1946, two years before the Marshall Plan was even signed. Moreover, the NHS was funded by direct taxation and citizens' contributions to national insurance. These plans, too, were drawn up before the Marshall Plan was signed, and the possibility of receiving US aid never figured into them.

I would also add— though I leave it to a proper economic historian to clarify this point exactly— that the Marshall Plan was largely (though not completely) implemented in the form of dollar aid, eg, it gave European countries block grants to purchase essential goods from the US. Funding a nationalized health system would not have been in the program's remit.

Further reading— Charles Webster, The National Health Service: A Political History (Oxford, 1998); Nicholas Timmins, The Five Giants: A Biography of the Welfare State (William Collins, 1995); Jim Tomlinson, “Welfare and the Economy: The Economic Impact of the Welfare State, 1945-51” Twentieth Century British History 6 (1995): 194-219.