The obvious off-road routes are the regional and national trails, which includes the Icknield Way and the Peddars Way near me. There's a map of Peddars Way with accommodation finder on
https://www.nationaltrail.co.uk/en_GB/trails/peddars-way-and-norfolk-coast-path/trail-information/ and Ickneild Way Trust have a more basic website at
http://www.icknieldwaytrail.org.uk/
You could start with the Ickneild Way and Peddars Way, then link the north end of Peddars Way all the way back around via Ness Point by the Norfolk Coast Cycleway (NCN1 / RR30) and Two Rivers Route (RR30) which are mostly tarmac but fairly pretty (apart from central Lowestoft!) and then return towards Cambridge by another route, maybe NCN13 and 51?
Edit to add: or you could return from Peddars Way along the North Sea Coast Route NCN1 and then see how much of the Fen Rivers Way is cycleable - I know parts are, but I've not checked the footpath/bridleway/byway split.