Many thanks to both of you for your advice.
We've always had Springers before, so Bassets will be somewhat different! A whole lot less springy but more stubborn, I suppose.
I plan on containing him in the kitchen until he gets the pee thing. As you say, it's nearer the back door.
He has only ever lived in a kennel in the garden, so he is used to going to the toilet outside. Hopefully, that will help.
My only apprehension is that his current owner says the reason he is outside almost 24 hours a day is because whenever he goes into their home, Harvey goes to the toilet.
But he hasn't been toilet trained.
He is also intact. Someone has suggested that neutering normally stops a dog peeing if he's doing it as a territorial thing.
I suppose we'll just have to wait and see. I'm expecting the worst (pee and poo all over the kitchen) so, hopefully, what we get will be a bonus! 
Thanks for the cheese tip - as you suggest, a tasty reward encourage him to understand.
I've bought him a Kong thingy so I can stuff it with edible goodies to help with any urge to chew - plus it should occupy him for an hour or two (maybe!). He's not yet two years old, so I imagine he may still be wanting to chew.
I'm working on the theory that a Basset is stubborn, has selective hearing, terrible wind, can be lazy and he will eat all foodstuffs if allowed - sounds as though Harvey will get on fine with both my DSs. 