So many great suggestions!.
Yes, use Tesco vouchers and Too Goid to Go to eat cheaply.
Markets, Borough, Portelbello, Spitalfields.
Museums, the Brands Museum is a paying museum but really lovely, looking at how brands and packing have changed. Science Museum is good fun.
Walking, all the big parks. Boat or DLR to Greenwich Park and Market. Walk through the foot tunnel, by the Cutty Sark, under the Thames.Walk along the Thames round Southbank. Walk at Greenwich to the O2and have a look around. Get the cable car over the Thames. You can go to the Flood Barrier at Charlton.
Graveyards, Nunhead Cemetery and Highgate are beautiful for walking round.
DLR, tubes, Elizabeth line all great for cheaply travelling and seeing lots of London .
Outside of central London, paying bit not expensive are Chislehurst Caves. Interesting and amusing tour. Caves were used for gigs and as air raid shelters in the past.
You'll be able to find lots to do which won't break the bank. Have a wonderful time.