Double mattress - for a bad back (EH7 Leith)

I'm currently living in an old motorhome for a month, in between houses, but the old mattress is killing my back and I can't afford a new one.
I would be forever grateful for a comfortable, medium firm double mattress 190x140cm that's not very thick - ideally 15cm. Memory foam or similar. From a non-smoking home cause I'm allergic to smoke. But not to pets, thankfully. :-)
So if you have recently bought a new bed and have a decent double mattress to dispose of, I can collect from anywhere in Edinburgh. Any time this week.