This is the National Cycle Network's Oxford-Cambridge route (aka the Varsity Way), but there's more to it than that.
From Oxford, through Milton Keynes, to Bedford, it's mostly minor roads - some of which can be busy at times - connected by occasional traffic-free paths, particularly in MK.
Bedford-Great Barford is a fine railway path, and St Ives-Cambridge an exceptional one, the latter buttery smooth tarmac beside the new Guided Busway.
The route continues on minor roads after Cambridge, crossing Suffolk on an enjoyable itinerary that takes in several market towns before reaching the coast at Felixstowe. There's a final dogleg back to Colchester from here.