Length: 16¾ km (10.4 miles), with longer and shorter options. Toughness: 2/10
10:12 Shepperton train from Waterloo (Vauxhall 10:16, Clapham Jct 10:21, etc), arriving Norbiton (in TfL Zone 5) at 10:38.
Return from Hammersmith is via underground (or bus). The walk document lists several mainline stations as earlier and later finishing points, but there are fewer services than usual this weekend. If you carry on past Hammersmith head for the mainline station at Putney (trains at xx:04, xx:29, xx:34 & xx:59) as there's no District line service from Putney Bridge. If you want to finish the walk earlier there's a replacement bus every half hour from Chiswick & Barnes Bridge to Barnes, connecting with trains via Putney to Waterloo.
The first part of this walk is through Richmond Park, and at this time of year it should be worth putting up with the Bank Holiday crowds in the Isabella Plantation to admire the Kurume Azaleas. It's quite a bit further to the suggested lunch pub – Sun Inn by the village pond on Barnes Green – but you could break for mid-morning refreshment (or a picnic lunch) at the park café near Roehampton Gate.
Unless you drop out at Barnes the afternoon leg is along the north bank of the Thames, with a short diversion inland to visit Chiswick House & Gardens (free entry to the gardens, but £12.50 if you want to visit the house and aren't a member of English Heritage or have a National Art Pass). There's another drop-out option of diverting to Chiswick or Turnham Green, but the full walk continues along the Thames Path to Hammersmith and (optionally) onwards to Putney. There's a café in Chiswick House and plenty of other refreshment places wherever you choose to finish.
You'll need to bring the directions from the L=swc.261 . A fair proportion of the walk is on firm surfaces, so choose comfortable footwear.