There are a lot more recommendations I could put on here, but trying to limit to 10 and based on actual experience as well as word of mouth...
Ask at any of these & they'll recommend others too.
Coffee Shop · Holborn and Covent Garden · 267 tips and reviews
Mark Ashbridge: Pitch up at the 'brew bar' and taste a thing or two. Head Barista, Dave Regan, is a dreamboat. If you're on a coffee crawl, Dept of Coffee & Social Affairs is right across the street.
Coffee Shop · Kensington and Chelsea · 54 tips and reviews
Mark Ashbridge: Go West! Great spot in the West of London amongst it's slew of chain coffee shops. The manager, Isa, is also the UK Aeropress champion.
193 Wardour St (btwn Oxford St & Noel St), Soho, Greater London
Coffee Shop · 271 tips and reviews
Mark Ashbridge: All the TAP shops are beautifully pointed, this one has the added excitement of Tapped & Packed's roaster down at the back. Also in close proximity to Kaffeine for those on a coffee crawl.