Your route out of london to Shere looks fast but not so much fun. Here's a route makes getting out of london a bit more interesting and avoids hills. The countryside from Cranleigh to Midurst is a bit boring though.
If you do want to go via Haslemere, here's a prettier route that follows a Surrey Cycle Route from Shere to Haslemere. There's a cycle path along the section of the A3 from Liphook to Longmoor camp, and another little section that allows you to avoid Liss a little further on. That should be all the A3 you ever want.
Your route out of london to Shere looks fast but not so much fun. Here's a route makes getting out of london a bit more interesting and avoids hills. The countryside from Cranleigh to Midurst is a bit boring though.
If you do want to go via Haslemere, here's a prettier route that follows a Surrey Cycle Route from Shere to Haslemere. There's a cycle path along the section of the A3 from Liphook to Longmoor camp, and another little section that allows you to avoid Liss a little further on. That should be all the A3 you ever want.