Matt, I'd suggest doing small orders rather than 1 large order. It may work out cheaper for the shipping, plus smaller packages tend to get overlooked by customs. One large order probably won't and you'll get hit for VAT & customs duty.
What I do is put you items in the basket and then every few items, go to the checkout and check shipping costs to the UK.
Also, ordering sets can be better that reels as again they'll be smaller packages and cheaper to ship.
Babolat Strike 18 x 20; Wimbledon stringing team since '04; Head Wimbledon stringer '14 - 15; Babolat stringing team '10 -'15;Twitter @therqtstringer