Planes and boats and trains... and taxis..and wheelchairs and walking...and buses
Comprehensive information is to be found at VisitLondon
You can get express (surface mainline) trains to the central terminals. Paddington for Heathrow, Victoria for Gatwick, and Liverpool St for Stansted.Visit London's airport transfer information page details the options
You can get taxis.I advise you to only use London's black cabs who are all licensed. Approximate fares can be found at Transport for London. Taxis accommodate a minimum of 5 people, and there are also 7 seaters. Transport for London have a list if you wish to prebook.
AROUND THE CITY
Walking is without doubt the best way to take it all in and really experience the capital. But don't be deceived as to the possible distances. Central London consists of three separate cities, The City, Westminster, and Southwark. It can make sense to plan sightseeing accordingly to reduce unneccesary use of transport.
Detailed advice can be found at the VisitLondon website. From transport to hotels, to toilets, shops and attractions, this is a very useful body of information. I am pleased to advise disabled visitors and guide to maximise time in London.