Length: about 13km (8.1 miles). See † below for a longer walk to Tonbridge. Toughness: 1/10-2/10
Southern Uckfield train from London Bridge at 10:07 calls at East Croydon at 10:22 and arrives Hever at 10:49.
Return trains from Leigh are at xx.05 to London Victoria (change at Redhill, arrive xx:33 depart xx:40) and xx:26 to London Bridge, Waterloo East and Charing Cross (change at Tonbridge, arrive xx:31 depart xx:37).
The walk notes suggest an “Any Permitted” return ticket to Leigh (Kent). In practice on-board Southern staff have always accepted a Leigh ticket on the outward leg but you may be asked to pay a small supplement for one stop from Edenbridge Town to Hever.
This route mostly follows the route of the Eden Valley Walk with a short detour to Leigh towards the end. I've picked this route because it provides a short walk which is mostly along firm paths. To finish at Leigh, at Point 37 (the "Straight Mile") in the written directions, when you see the concrete bridge on your left, turn left over it switching to Point 51 of the Book 1 Walk 19 Hever to Leigh route for the short stretch to Leigh.
Lunch is in Penshurst, where you have choice between The Leciester Arms (online booking recommended/possibly required) or The Porcupine Cafe at Penshurst Place (+44 (0)1892 870307). For end of walk refreshments, there is the Fleur de Lis (01732 832283), a village pub close to Leigh station which serves food and drinks, including tea and coffee.
† For a longer walk of 16 1/2 km (10.3 miles) you could continue to Tonbridge on the full main walk, where there are plenty of refreshment options dotted around the High Street.
You'll need to bring the directions from the L=swc.345 page. Unless you plan to walk to Tonbridge, you'll also need the directions from Book 1 Hever to Leigh page for the short detour to Leigh