Well first of all, most British politicians do support Israel and a sizeable portion of their citizens to as well.
But you have to understand that politically, Britain has done a complete 180 degree turn politically since the 40s. Even though their country does support Israel, they don't want to have the appearance that they do for political and social reasons (all the psychotic Muslims in their country and to avoid hatred directed against them by the world community).
I guess you can say that they left the responsibility for supporting Israel on the US, but we took the job gladly. Britain, France, and even Germany also give Israel all kinds of aid and cooperation, but they intentionally don't publicly support Israel because they want to dodge the bullet from all the angry Muslims in the world.
Hell, even alot of Western Europeans are completely unaware of the history of Israel and how their country participated in its establishment. So they just blame the US only, yet covertly support Israel just as stridently as the US does.
Thats what Europeans do, they are scandalous and calculating.