25 cents to 1.25 euro for coffee and 1 euro for a beer today, but I am in Porto rather than London.
In London, in fact any city, I always prefer the shop option.
Buy a couple of bottles (I always carry a bottle opener in my day bag), some crusty bread, the best filling for my liking (I have a small knife too), sit on a bench somewhere & soak up the culture.
If it's raining, then a seat on any nearby station usually does it for me.
Pubs are ok, but not regularly for people on a tight budget.
Weatherspoons & Yates's both do different specials on each day & for the money, they're quite good value. Check out 'A pie & a pint' for (I think) £5.

Try Wetherspoons chain for cheap beer and cheapish hot food.. Try Subway for a chap breakfast roll and coffee.
As others have mentioned suck all the free museums and galleries dry and I always donate what I can. You could donate a tenner across three sites a day and still stay within budget or bu they taking home trinkets at their shops.

Thank you all for your help and suggestions! My wife and I are about halfway through our time in London and have had a fantastic experience so far. We saw a show at Shakespeare's Globe today for £5 each today in the groundling standing area. Have loved the cheap food choices and the free museums have been incredible. Biggest single expense have been our travelcards but the commute through the city has been pretty painless. Again, thank you!

Beer has been expensive as has been said on here...found myself drinking a £6 Czech beer and decided to just wait until we're in Prague for the beer - price is not worth it!
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