Don't forget you can always fly to a smaller, cheaper airport on the outskirts, then get a heli transfer into Battersea Heliport. While it's not always the most convenient point, it's a lot closer to London than Luton, Stansted etc.
Various operators, depending on your budget & number of pax
PremiAir
www.premiair.co.uk (AS355, A109E, B222, S76)
Starspeed
www.starspeed.co.uk (AS355, EC135, AS365, EC155)
Harrods
www.airharrods.com (A109E/S, S76, S92)
Helicopter Services
www.helicopterservices.co.uk (R44, B206, AS355, A109C)
London Helicopter Centres
www.london-helicopters.co.uk (EC120, AS355)
Rotormotion
www.rotormotion.com (A109)
...to name but a few...