If it's a nice day you should do both. Start off at Borough Market and get yourself some food. Walk along the South Bank and cross the river using either Waterloo or the Golden Jubilee Bridges. Waterloo has traffic, but it also has the best views of the river, as it's on a bend and you can see far in both directions. It's particularly good at sunset. There are two Jubilee bridges, either side of the Hungerford railway bridge, which gets in the way of views. So you can only see one direction or another. No traffic though.
It's a five-minute walk from Victoria Embankment (the North bank) up to Covent Garden, where you can look around the shops and get yourself a tube back to LHR.

Of course, this assumes you like walking. Personally, I walk everywhere in London where I can. Usually quicker than the tube for short distances, especially where changes are involved.