The Class D airspace for London City is accessible. Now that I've said that, there will follow a series of posts from various contributors giving their opinion whether you should be in there with a SEP or not.
From Biggin, the best scenery is probably along the River Thames and into Kent. You can head North to the QE2 Dartford Bridge (keep the bridge to your left to stay outside of the London City Zone) from where you'll have a good view into the City of London, then follow the Thames East. You can see the port of Tilbury, Henry's fort at Tilbury, Gravesend, the industrial sites of Canvey Island, SS Richard Mongomery (if you can pick it out - it can be done!), the Medway Towns, Southend Pier, Leeds Castle, Dover Harbour and the white cliffs, Hastings, Folkestone, Rye, a bit of the South Coast, then return to Biggin via Bewl Water and Tunbridge Wells.