The info sharing between MI6 Mossad and CIA is much deeper than one might think. At the end they are part of the same kind of cause. Yes either the British knew it or, if they did not know, they were immediately given the full details of what kind of mess happened, by Mossad. Germans migh have been invited to share the info at a rather initial stage too, an France of course, probably a little later.
U.S. State Dept. 'deeply concerned' about Israel's approval of new settlement construction (Reuters)
from the article: Britain 'knew Mossad was using fake passports for Dubai hit'