Paul,
Best way to minimise the taxes is to depart from Gatwick rather than Heathrow as the airport tax is GBP 20 cheaper at LGW rather than LHR. As mentioned above its easier to arrive into LHR and hop on the underground to get into Central London ( depending where you are staying ). Best bet is to pick up an Oyster card at the LHR underground station. You will pay a GBP 5 deposit on the card but you get it back if you hand the card in when you've finished with it ( see www.tfl.gov.uk/oyster ). Using the Oyster cards means that you always get the best deal when using any the underground or buses and will never work out costing more than the individual one day travelcards. You can top the Oyster card up with cash or credit card at many shops and also at virtually every underground station. Don't use the Heathrow Express as its very pricey and only gets you to the outskirts of London.
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