The Age of Austerity; from the end of the war in 1945-1951, the British Empire went through a period of depression, a loss of huge amounts of wealth.
It is most probable that the British didn't have the funding needed to maintain their standing in computer science. The U.S. didn't have the same financial limitations as the British after WWII, largely because the US had a more diverse and healthier economy.
The US was able to gain its dominance through not only a healthy financial situation but also through their competition with the Soviet Union after the war. Much of modern computer science can be contributed to the Cold War and the Space Race. The need for computer science greatly expanded in the US during the Cold War.
https://en.wikipedia.org/wiki/Economic_history_of_the_United_Kingdom