Amazon and eBay are extremely convenient. Most people have an account with these companies and are familiar with online shopping. But where else can you buy, if these websites don't have the exact book in stock and delivery within a few days?
Some great UK online shops for paper piano books...
Music room- superb range of books and delivery within 1-2 days (I've bought many from them, always prompt delivery)
Sutton Music Store- in Sutton High Street (SM1), try before you buy by playing the music on their in store pianos, free local delivery.
Digital sheet music for ad-hoc or supplementary pieces...
Sheet music plus- gigantic range of digital sheet music, instant download.
Musescore- free digital sheet music, original compositions and arrangements.