As per JoeM says you can go Thames Path to Weybridge, then Wey Navigation Path to Guildford.
Then ride through Guildford town centre following the WNP, past the White House pub, cross 3 small bridges until you get to a wooden footbridge over the River Wey, cross over the bridge then cycle over the sports fields, cross the main road (A281 Shalford Road) and cycle up Pilgrims Way until a tight left hand bend.
Turn right into Northdown Lane following the bridleway signs. This will take you up a steep climb onto Pewley Down. Ride along the top of Pewley Down then take the BW on the right (just after the wooden bench) that follows the fence line down the hill and follow that all the way to the bottom of the hill where it crosses a B.W.
Go straight across (through the woods) and follow this until you get to Halfpenny Lane, straight across here following the North Downs Way, over St Marthas Hill. Cross Guildford Lane and get on the Pilgrims Way B.W and follow that until you get to Water Lane byway. Climb this and your at Newlands Corner.