Not UK, but close enough and verified on Digikey's site:
You will have to pay VAT as usual on any imported shipment, but as long as you specifically order in GBP, there will be no additional fees or charges; you'll simply get a bill from UPS (probably) with the VAT charge; it arrives a couple weeks later or so. If you order £1000 worth of components, your total extra charge is £200 (assuming you guys still pay 20% VAT on everything).
Also note the free shipping above £50.
All in all, it's pretty transparent and convenient - no extra fees or a pile of fuss, just the initial charge + the VAT charge some time later. Should arrive quickly too.
Do be sure to use GBP when shopping, and the .co.uk domain. If you order in USD (yes, even if your card is in GBP), you WILL probably get hilarious, nasty extra charges.