Take a helicopter.
Zone entry at Banstead, H7 to Barnes with altitude dropping to below 1,000 ft. H4 along the Thames right through the city of London, with fantastic views all around. Past the Olympic site to Isle of Dogs, then vacate the zone due South, skirt around croydon and back to Biggin. 45 Minutes.
http://www.caa.co.uk/docs/7/20100316LondonHeliChart.pdf
Otherwise, close on your doorstep could route overhead Chartwell
Visitor information - National Trust (slightly tight for airspace), overhead Hever Castle
Hever Castle | Kent | The childhood home of Anne Boleyn and back (15-20 minutes).
Further East, Leeds castle is fantastic from the air
Leeds Castle - The Loveliest Castle in the World, Kent, England.
If you go West, you can go overhead Michael Kane's place (edge of Leatherhead), Chelsea's training ground (cobham), then the disused Wisley airfield at Ockham (
Wisley Airfield - Wikipedia, the free encyclopedia) and past the semaphore tower
Explore Ockham Common, Chatley Heath and the Semaphore Tower | The Wildlife Trusts and Wisley Gardens (
Wisley / RHS Gardening) then head South to Dunsfold (Topgear track) before following the vally back to Biggin. 50 minutes.
Enjoy Surrey and Kent