Merchants Tavern is close to Old St tube, which is still zone 1, but not utterly central. I could make any restaurant in zone 1 work.
I think the NPM/Farr offer is one bottle per person but was only in January. Might be waived for the first Monday in Feb though!
There are quite a few places that do corkage for c. £20/bottle, but I’m not aware of any not listed above that’s £5 or less.