At the time Winston Churchill was right - the consequences of the "West" attempting to assist such an uprising would have been very poorly received in Moscow, with potentially dire consequences for entire world - let alone East Germany.

From another article on the anniversary:

"Most historians have accepted that the West's options were limited. Britain was worried about events inside Russia, then convulsed by the power struggle after Stalin's death. There was also fear of resurgent German nationalism only eight years after the Second World War."

I think that the content of the first two sentences quoted above had greater impact on the thinking of both Britain and the USA, than fears regarding German reunification.