Fernández & Wells (Mayfair)
This café is inside a clothes shop, or an "Emporium". The quality of the flat whites depends a lot on the barista that makes them... I have had great flat whites with strong coffee body, right temperature, foam... and then a very milky one that seemed more like a cappuccino than a flat white. Mind you, it was still a very fine coffee drink, but certainly not a flat white!
They also have the usual snack selection from Fernández & Wells, although I haven't tried it here. Tables seem comfortable enough to use a laptop on them for a while, but I didn't see any power socket. Wi-fi was free and functional for browsing with my phone, I used it because cell reception is a bit weak on the building, but I haven't used it with a laptop or tested it "work needs".