Rutland is an option if you just want to ride. I live a few miles from Peterboghorror and sometimes use it as a bit of a training ride. It’s fairly undulating (but not hilly) and nothing at all taxing. Similar to canal path trails really.
Peterborough to Thetford is about 1hr 20 mins (i generally get there once a week). Best route is get on the A47 through Thorney to Guyhirn, then left to Wisbech and then right on the A1122 to Downham Market and onto Stradsett. Turn right onto the A134 and then finally onto the A1065 at Mundford to Brandon. Once in Brandon you’ll go over a level crossing. Carry on to the traffic lights, turn left and then follow signs for Brandon Country Park. It’s free to park, whereas high lodge will cost you about £5. There’s a tea room there and most of the unmarked trails go from there. Or you can follow the blue trail (back out of the car park and across the road) which will lead you over to High Lodge where you can pick up the red and black (which aren’t really red or black, but fun nonetheless).
The hidden trails are much better than the routes, but it might be a bit of a chore finding them to be honest, although a lot of them are fairly obvious due to the winter race series.
If you don’t fancy those country roads to get there, you can always go A1/A14/A11 – will take a little longer, but much easier to navigate.
An alternative would be to go to Cannock Chase and do a few laps there? Or as already mentioned, a bit of a detour and your in the Peak district for a bit of a ride.