Lovely flat ideally located to visit London!
You can walk to a lot of places (Tate Modern, Millenium bridge, London Eye...) and there are lots of restaurants and bars on Queen's walk.
For transport (we were with 10&12 children): we mainly used the Southwark station on Jubilee line (5 minutes) and RV1 or 381 buses (Tower of London, Tower Bridge, Borough Market, Sky garden...). From/to St Pancras station, we used 63 bus (few minutes walk from the flat and less than 30 min to reach the station).