I guess it depends where you want to go to!
If you are on a budget and don't want to take the tube or Heathrow Express try hotelink who offer a scheduled hotel transfer service from both Heathrow and Gatwick Airports. Their URL is www.hotelink.co.uk. Please note that they don't service every hotel in London so do check with them that the hotel you are staying at is on their service schedule.
Hotelink for six people is more expensive than a taxi cab
Which airport and which hotel?
London does have more than one airport.
If you're arriving at LHR, the least expensive way to get from there to central London is the tube. If you fly in to T4, you'll have to take either the free Heathrow Express shuttle between T4 and T1,2,3 then walk to the tube station there or a free replacement bus service from T4 to Hatton Cross - there's no tube station at T4 until next September because of construction of the new T5.
Once at the tube, a single ticket to central London will cost £3.80 for adults, £1.40 for children. There are no lifts or escalators at Hatton Cross, but there are TfL staff who can help with luggage downstairs to the platforms.
The tube to central London will take about 45 minutes to an hour, depending on your destination. Because LHR is the start of the Piccadilly line, you can get seats together and find enough room for your bags without too many other passengers around.
If you need to transfer to a District line train, the easiest transfer is at Hammersmith, where the eastbound lines are across the platform - maybe twelve steps from one to the other.
Do please let us know which airport and which terminal you are flying into as well as where exactly you are heading to as this will determine the best route by public transport as well as the cost of a private car hire.
You may well find it cheaper to get a private van and driver to meet you, help with your luggage and take you door to door to your destination. You can google London Airport Transfers to get an idea of cost.
Thanks so far for the advice. Heathrow airport and at terminal 4. I'm still confused...
I just found this excelent site for airport transfers for airports all over the world.