“What’s the best place in Greenwich/Blackheath to off-load unwanted books for cash?”
Hmmm. Now, for cash, that’s a tough one. Are they specialist, antiquarian or locally-related? If so, you might be able to interest the second hand book shops around here – Bookshop on the Heath, Halcyon Books or the recently re-opened Greenwich Bookplace and Gallery – far fewer than even ten years ago now, and, necessarily due to their size if nothing else, pretty picky about what they take.
If they’re novels or general all-purpose non-fic, I doubt if they’ll fetch much. You might try taking a stall at Greenwich Market – it’s a tenner during the week. They’re not taking on any more jewellery or food stalls (and judging from the amount of marble coasters available just now, I suspect there will be a moratorium on them soon, too) but books still seem to be okay.
To be honest, I take most of the books I have persuaded myself to let go of to local charity shops or, if I’m really organised, to a charity booksale. The obvious local one is Amnesty International whose next sale is 18th June, so you’re in good time. Of course the real problem is to discipline oneself to take the books to the storage facility and then not return on the day of the sale to buy more than you donate.
If you’re sure you want to sell, then a longer-term solution is online. Try Amazon marketplace or my pal who takes buying and selling things on the internet very seriously recommends Gumtree as a better, cheaper alternative.