Are you wanting to run from where you're staying, or catch a tube/bus there? Will you be running in daylight or when it's dark (some parks shut at dusk and some paths are not lit)?
I'd avoid the South Bank as it can be really busy with tourists, but you can run along Embankment to Parliament Square, then turn right and you're at St James's Park. A loop of that will get you to Green Park, and a loop of that will get you to Hyde Park and Kensington Gardens.
An alternative would be to run in the opposite direction to Limehouse Basin, up Regents Canal to Victoria Park. From there you can do a loop of Victoria Park and if you want, cut via Hackney Wick across to the River Lea Navigation by the Olympic Park. You can do a quick loop of that or head up the towpath to Coppermill Lane and back down through the nature reserve (you can see where this loop goes on Strava on the long run I did at the weekend).