It might be out of the way for most people but Norwood Park next to Crystal Palace is a gem. Big park with amazing views of Central (think Primrose Hill but southern aspect) and ridiculously quiet, even on a lovely day.
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The Avenue Gardens area at The Regent's Park has a lovely shaded stretch with lots of benches. I don't have the best photos, but it's beautiful in person.
That looks lovely, might have to dig my Ricoh Z1 360 camera and do some digital photography there.
Richmond Park is the obvious pick, if you're looking for wide open spaces.
Gunnersbury Park in Ealing/Acton, the perimeter path of about 2 miles, is almost entirely shaded. Nearest tube Acton Town.
Crystal Palace Park (though shout out to the Norwood Park comment!). There's just so many different areas to the park, good for those wanting some shade (like me!)
Battersea park has a fair bit of shade, but it can get very busy, especially when the weather's nice.
That sounds like a good idea, how easy is it to get to from the Battersea Power Station underground exit?