Length: 18 km (11.2 miles), or 15¼ km (9.5 miles) with shorter afternoon. Toughness: 3/10
10:15 Hastings train from Charing Cross (Waterloo East 10:18, London Bridge 10:24, Orpington 10:40, etc), arriving Tonbridge at 10:58. Buy an “Any Permitted Route” return to Penshurst, which in theory will get you through the ticket barrier at Tonbridge.
From south London you could also travel out via Redhill. You'd need to connect with the 10:26 service which gets to Tonbridge at 10:56. If you do this, buy a return to Tonbridge.
Unless you switch to the Circular Walk and return to Tonbridge, trains back from Penshurst are hourly in each direction. It's quicker to return via Tonbridge (at xx:48) but your ticket is also valid for travel via Redhill (at xx:34).
The first half of this walk is a fairly gentle stroll along the Medway valley, including a stretch through Haysden Country Park where a closed bridge and other disruptions mentioned in past comments have all been fixed. It should be possible to get a pub lunch in the beer garden of the Leicester Arms Hotel in Penshurst village, but if this doesn't appeal you could visit the Porcupine Pantry outside Penshurst Place or have a picnic in the churchyard.
Regulars will know that Penshurst station is nowhere near the village, and there's a choice of two routes to it in the afternoon. Both go via Chiddingstone which has two good tearooms: the Tulip Tree in the village or the one at the back of Chiddingstone Castle (although access to its tearoom might be restricted as there's a “Circus of Curiosities” event in the grounds). There's still a fair distance to cover to Penshurst station but if you misjudge your arrival you can pass the time in the Little Brown Jug across the road.
You'll need to bring the directions from the L=swc.235 page.