Burpham is where the current A3 diverges away from the old A3, now the A3100, into Guildford. It is quite a handy shortcut compared to the mayhem the A320 and the A322 routes into Guildford sometimes are, but it is signposted as a local route from the A3. It isn't even given a number.
Before the A3 bypass was constructed, Clay Lane used to run along what is now Burpham Lane and Bowers Farm Lane. It now goes over a nice wide bridge where the slip road to the A3 Northbound is. Most of Burpham was built at this time as well, which is why it seems the estates fit quite well next to the route of the A3