Length: 15 km (9.3 miles) plus whatever you add on in Highdown Gardens. Toughness: 2/10.
10:17 Littlehampton train from London Bridge (not Victoria; East Croydon 10:32), arriving Angmering at 11:48.
Or take the 10:02 Brighton train (Clapham Jct 10:09) from Victoria and change at East Croydon (arr 10:19, dep 10:32) for the Littlehampton train. Note that there are fewer trains than usual out of Victoria this Sunday.
Direct trains back from Worthing to East Croydon and London Bridge are hourly at xx:35 (to 20:35). There are others to Brighton at xx:39 & xx:55 where you can change. Buy a return to Angmering, which is also valid via Brighton.
Apologies for the long train journey, but now that winter seems to be loosening its grip I'll sometimes deviate from my usual choice of a walk in or around London and venture further afield. This one is a double variation of the Arundel to Goring-by-Sea walk, with a much shorter morning leg consisting of a gentle climb to an Iron Age hill fort, followed by an extended afternoon stroll along the seafront from the Goring Gap to Worthing. The main attraction in the middle of the walk is Highdown Gardens (free entry), with its fine collection of exotic trees and plants. At the end of the walk you can sample Worthing's seaside attractions, including a stroll out along its pleasure pier (also free).
If you want a pub lunch you could try The Highdown (01903-924670), a large Brunning & Price pub just outside the gardens. Alternatively, carry on for half an hour to the Bulls Head, a Chef & Brewer pub in Goring-by-Sea. Both serve food all day. There are plenty of refreshment places in Worthing, including the comfortable Railway Hotel outside the station if you've got time to kill before the train.
Please bring the walk directions from the L=swc.295.ax page, which includes a map of the gardens.