This list for Shoreditch isn't bad but I wouldn't consider "Look Mum, No Hands" to be Shoreditch; it's more like Clerkenwell / Farringdon. Nonetheless, it's a great spot, and weirdly bike-oriented. Feels like Seattle. Grind! is also pretty cool. I'm not sure any of the Dept of Coffee and Social Affairs spots survived COVID. I know the one on Liverpool St is now Attendant and it's good. Their Clerkenwell location is also in a really cool spot on Leather Lane.
Probably my favorite area for coffee, anchored by Monmouth Coffee Company. Excellent quality coffee, really top notch. Buy a bag of beans vacuum packed to take home. Seating inside and out in one of the most interesting tourist-watching areas.
Second prize in that area goes to Fabrique, which I believe is a chain started in Stockholm. Very small location on Earl St, between Charing Cross Rd and Seven Dials. Try the Cardamom Bun with your latte / cortado. Start at Foyle's bookstore cafe (5th floor), and then make your way to Fabrique, and then to Monmouth. 5 min between each and you'll be pleasantly overcaff'd.
The Camera Museum, near the British Museum
Knockbox and Redemption Coffee are both on one of the most interesting little side streets in the area, Lamb's Conduit, connecting Corum's Field and the Great Ormand Children's Hospital with Holborn. Both are small but great, and the other quaint little shops are worth a look too.
A number of those already covered, including Grind, Attendant, and Fabrique are near here. But, for something different, try H.R. Higgins. Grovenor Square and the American Embassy are near by. Oh, and apparently Higgins was "The Queen's Coffee Man"
Beany Green, in Little Venice behind Paddington Station. Plus, you get to see all the little boats on the canal.
NOTES. The Trafalgar Square / St Martin's Lane location is my favorite. There's some seating at the window to look out toward the square and the Nat'l Portrait Gallery, and seating at large tables in the back. Coffee is great, but there's also breakfast in the morning (at least on weekends, not sure about all week) and tapas / charcuterie and wine in the evening. It's an all-around hit.
OK, my favorite, with considerable bias, is Moon and Maybe, on St Mary's in Ealing. It's a cozy little spot with great coffee, a pocket courtyard behind when weather is good, and cocktails on Friday and Saturday night. It's also owned by two dear friends of mine, so excuse the gushing.