The busiest route out of the UK is now London – Dublin, and infact this is now the busiest international route in the world. In 2005 there were just over 4.36 million passengers between LON and DUB, by comparison JFK attracted 2.94million and Palma attracted 1.21 million passengers. The other major spanish route, Malaga attracted just under 2 million passengers. As correctly stated earlier LON- Paris was formerly the busiest route, but Eurostar saw to that!
P.S. If you add EWR (Newark) onto the total then that adds another million passengers out of London. But remember that overall New York is not as well served as Dublin from the regions and the Dublin routes from the regions generate some large passenger volumes. So overall DUBLIN is the largest destination from the UK.
BTW, IF you meant which actual route (rather than city pairs) was the busiest then yes LHR – JFK moves into number one spot, with basically all of the demand in 2005 passing through LHR, compared to only 2million passengers going LHR – DUB.