Many 2nd hand white goods retailers buy in their stock dirt cheap from house clearance companies, or as pallets of cosmetically damaged goods, not the public unless they happen to be running low on particular items.
Generally they'd only be interested in the collecting from you and buying, if you have something exceptional. IE: it's very new, or Smeg etc, or a double unit modern fridge freezer, or are happy to pay them to collect.
You need to stay local to reduce transport costs, but here are loads of small wheeler dealer 2nd hand white goods shops in 'cheaper' bits of London if you go looking.
But, IME the 2nd hand white goods market is one where you have to know what you're about and be quite robust as a woman.
I have managed to sell but it's by turning up in a van with clean goods in the back, and accepting relatively low offers in order to get shot of them.
To get best deals I'd advise you to know exactly what model, age, and have receipts to prove, fully expect to get knocked down, and have a 'take it or leave it attitude' if they take the Micky.
They may not be interested, but can recommend these guys as the nicer end of it all - Black horse domestic appliances - 1 Blackhorse Rd, E17
Don't know if these guys actually have a name, but they're long term - 196A Philip Ln, N15
Bit marmite but: - AJ Links appliance center -163 Trafalgar Rd, London SE10