Length: About 12 km (7½ miles). Toughness: 1/10
Meet in the ticket hall of Richmond station at 11:00. Either take the 10:39 Bracknell train from Waterloo (Vauxhall 10:43, Clapham Jct 10:49, Putney 10:53), arriving at 10:58; or the Overground or a District line tube (see the TfL site for times). Richmond is in Zone 4.
There are five trains an hour back from Richmond to Waterloo (at xx:05, xx:09, xx:27, xx:37 & xx:57), plus the Overgrounds and tubes.
This is one of those simple Thames walks: upstream from Richmond on the south bank, cross the river at Teddington Lock and return along the north bank. It's one of the prettiest riverside stretches in the capital with plenty of interesting sights along the way.
The logical place to stop for lunch is at the halfway point, with OpenStreetMap showing a couple of pubs and a café at Teddington Lock. The Walk Notes suggest The Anglers, a large Fullers pub which is doubtless crowded in summer but should be less of a squeeze in February. There are more riverside pubs in Twickenham on the return leg, and plenty of places in Richmond if you need reviving before the journey home.
You won't need the L=short.52 page for the directions but it has some useful information about the places en route. Of the free attractions Marble Hill House is closed for the winter but the art gallery at Orleans House would be worth a detour.
NB. The Walk Notes say that its ‘fly in the ointment’ is a long stretch of road walking between Teddington Lock and Twickenham, but the map shows a newish public footpath parallel to Strawberry Vale which would cut out a third of this (as well as giving a good view of the beautifully-restored Strawberry Hill House: see photo). The Walk Map also shows a simple out-and-back route between the station and Richmond Bridge, but for a small extension at the end you could continue along the Thames Path for an extra 1 km and cross the river at Richmond Lock instead.