Length: 13.2 km (8.2 miles). Toughness: 3~4/10
Take the Thameslink train towards Three Bridges (from West Hampstead at 09:29, St Pancras 09:40, London Bridge 09:55, Norwood Jct 10:08, East Croydon 10:13, etc), changing at Redhill (arr 10:31, dep 10:43) for the GWR Reading train, arriving Gomshall at 11:04.
Trains to Gomshall are every two hours, so if this connection fails you might want to have a Plan B up your sleeve: a circular walk around Dorking, perhaps.
Trains back from Box Hill & Westhumble are at xx:10 to Waterloo via Wimbledon, xx:16 & xx:46 to London Bridge via Sutton and Mitcham. These all depart Dorking 3-4 minutes earlier, if you choose to divert there. A return to Gomshall is valid for the return journey from either of these stations.
The section of the North Downs Way (NDW) between Gomshall and Westhumble is normally done as a summer extension to the Guildford to Gomshall walk, but Book 2 includes the linking directions from Gomshall which enable this shorter variation. It essentially consists of a steady climb up onto the downs, then a long stretch along the ridge before descending to Box Hill & Westhumble station via Denbies Vineyard.
There are no pubs on this stretch of the NDW but the directions point out some places where you could stop for a few nibbles. If you don't have a long break you'll finish before 2.30pm and could reward yourself with a large tea at Denbies or even a late Sunday lunch at the Stepping Stones Inn, a five-minute walk beyond the station.
Although much of this walk is on the well-waymarked NDW you should bring the instructions from the L=2.13.g - you'll only need the directions from the last four pages of the PDF download.