I suspect Cameron will be keen to avoid being hugged too tight, though. Much of Europe is talking about closer economic integration, with greater powers for the European Commission to supervise members' budgets and impose penalties on countries which behave imprudently. Cameron pays lip service to this kind of thinking in an FT article today, in which he writes, with the Swedish PM, that "there must be better safeguards against member states spending and borrowing too much". But the coalition is wary of anything that looks like dragging them, in any way, towards the eurozone crisis.
Some government types tell me that they see their role more as nudging Europe in the right direction, but largely letting them get on with it – like pushing a boat away from the shore. That is Cameron's challenge today, even if it makes Sarkozy and Merkel a little frostier to deal with.