If you can't go to the bar, let the bar come to you. A number of London bars and distilleries have diversified and set up cocktail delivery services, so you need not worry about getting your ratio of gin to vermouth horribly wrong.
Shoreditch bar Callooh Callay have classics including negronis and Old Fashioneds, and Hacha Dalston has your margarita and mezcal needs covered. If you're missing Ladies and Gentlemen, the kooky bar-in-former-toilets in Kentish Town you can order their Quarantini vodka martini among others (drinking it in the bathroom is optional). Alternatively The Drinks Drop have partnered with several different venues to offer their signature drinks as well as some lesser-known spirits like Dangerous Don Cafe, a blend of agave and coffee.