It's also faster than you might expect. European Union (EU) countries use three "channels" for customs processing. If you arrive from another EU country, whatever passport you hold, choose the Blue Channel once you've collected your luggage. Arriving from outside the EU, choose either the Green Channel - if you have nothing to declare based on the allowances outlined below - or the Red Channel, if you have goods over the duty free allowance.
The whole thing is based on an honor system. But keep in mind that, though it doesn't happen often, you can be stopped for a spot check in the Green or Blue Channels, and the penalties for breaking the law are pretty stiff.
Next: What you can bring to the UK from outside the EU