The whole pick-up-your-bags-and-recheck-them idiocy that they have in the US doesn't exist in the EU. We have a much nicer system to deal with international passengers arriving on intra-eu flights:

If you depart from a Schengen country, your bag tags will have a green lining (this is randomly applied to non-schengen flights as well depending on what paper they load, but they'll always be there on flights to schengen countries). If your bag has a green-lined tag, you can walk through a customs 'blue zone' if it exists, which means you can just walk through and no one will hassle you for stuff you might be carrying because it's all fine. If you don't, you get to do the normal pick between 'nothing to declare', and 'items to declare' depending on which category you fall into. Of course the green bag tags will signal anyone watching that you have nothing to declare anyway so most countries don't have a blue zone. Trying to go through the blue zone without green-lined tags is a recipe for having your stuff looked into of course.

The US doesn't have such a clever system, so they require everyone to pick up their bags, go through customs, and recheck them.


That all said, your bags won't have these lines because the UK did not sign the Schengen treaty. But because we have this wonderful system combined with airports that can actually keep apart international and schengen passengers (another thing the US lacks), you won't have to jump through any ridiculous hoops.