I use bikehike.co.uk. It can route using Open Cycle Map as well as Google. You can see it side-by-side with an OS map which is very handy.
Watch out if routing using Google – it’s knowledge of what is and isn’t a road can be a bit iffy, and on more than one occasion I’ve had a planned road route put me on a byway that would be a lot more fun on a mountain bike, and on another on a road that wasn’t even a through road (or a legal RoW). Having the OS map usually makes these things clear.
I’ve had a lot of success with planning routes this way even in unknown areas. Just spend as much time as possible on yellow roads on the OS map and it’s hard to go wrong.
I’d definitely recommend a GPS. Following a quiet route often means doing the opposite of what sign posts say, with lots of minor junctions. A GPS means you don’t have to stop to look at a map.