When you do get to a London Airport, Mainline Train or Coach Station
buy yourself, just like we Londoners do, an Oyster card -

it's the cheapest way to get around.

The Transport for London website is also a good overall guide.
 

London cabs are expensive but can be hailed on the street.
Mini-Cabs are cheaper.

Downtown Cars for mini-cabs from The Olde Salt Quay in Rotherhithe:
0207-231-0006
 
Getting to London Town Getting round London Getting to Olde Salt Quay
The Venues by Air Can offer / Need lift Maps and Postcodes