For the person that has everything or needs nothing, an experience gift might just be the perfect fit. Some of my favorite ones are offerring gift vouchers, including:

www.bisleyshooting.co.uk
Walking tour vouchers start at £20 / person
www.coutours.co.uk
Fragrance experiences starting at £49 /person
www.theperfumestudio.com

Shoreditch Street Art Tours — This tour always offers something different since new art shows up all the time and in the most unusual places. Think of it as live Where's Waldo, but the art you are looking for ranges from famous Bansky to C215 to piggy sculptures.
Public tour vouchers £20 / adult, £10 / child
Sweet Tooth Tours — Led by Le Cordon Bleu pastry chef Lynne Staartjes, Sweet Tooth Tours highlight London's best sweets (bakeries, chocolate shops, gelaterias), savories (cheese mongers) and more. Once you have tasted London, head to Paris where Lynne leads similar tours!
London experiences start at £58 / person (minimum of 2 for a private tour)