Let's see...
Let's say the UK lodges a formal complaint against the USA in the UN, being a security council member and all that shizzle. I'm pretty sure Russia and China would condemn the drone attack fiercely, just as they have condemned other foreign interventions by the US time and again, but that wouldn't get them far as the USA is also a member and can veto any penalty.
At the EU level though, most countries would side with the UK: at a baser level, the UK could expel US diplomatic personnel (and jail the spies), cease cooperation with US federal services for fiscal and criminal stuff, maybe become more stringent about US citizens' entry into the country. What about denying fly-over for any US airplane ? What about extending that ban all over Europe ? That would be a major inconvenience, especially for military operations. Same with maritime access... that could cripple US exports and imports really fast (just as it would cripple Europe's, sure). What about cancelling the 2003 extradition treaty ?
And then there's the population's attitude towards US citizens and representatives. As a french resident I still remember how french people were sometimes (mis)treated while in the US during the whole "freedom fries, must bomb Iraq" nonsense. I don't wish that on anyone.