Look up any offers you can. So for example if any of you are with O2 or have an Amex card, they do offers at places like Pizza Express and other chains. Especially for weekdays.
Lunch I’d avoid proper restaurants and stick to sandwich type places although even those aren’t cheap.
Obviously, avoid spending £££ on snacks and drinks - buy crisps etc from a local mini supermarket instead.
Sights - my favourite free things are the markets (Camden, Spitalfields, Borough, Portobello). Sky garden if you can get tickets. Horizon 22 if not. Walk down the Southbank, see the buskers, go to Tate Modern for free, cross over to St Pauls. Monument is cheap to climb but check opening hours. National Gallery, Portrait Gallery are free and the museums of course. Public river boat is cheap ish way to get a river trip - go from London Eye to Tower Bridge for example. Number 11 bus goes past a lot of sights too.
For shopping areas Regent St and Carnaby Street, Covent Garden, Coal Drops Yard up by Kings Cross.
Walk along Regents Canal from Kings Cross past camden market to Regents Park