We recommend that you use public transport if possible. Taxis from Heathrow or Gatwick will cost in the region of £60-£90. Do not travel with anyone offering a 'taxi' service inside the airports as they are likely to be illegal, unlicensed drivers.
From Heathrow Airport (LHR)
Take the Piccadilly Underground Line eastbound and change at Green Park onto the Jubilee Line. Then change at London Bridge to catch a overground train to New Cross or New Cross Gate.
Catch the Heathrow Express train to Paddington Station. Here you can either catch a 436 bus to New Cross Gate [this will take longer than the underground, but if you are carrying luggage, you avoid having to navigate station interchanges] or take the Bakerloo underground line to Charing Cross mainline station and catch an overground train to New Cross or New Cross Gate.
From Stansted Airport (STN)
Catch the train to Liverpool Street, then travel by Hammersmith and City Underground Line to Whitechapel. Change onto East London Underground Line to New Cross or New Cross Gate.
From City Airport (LCY)
Take the DLR train westbound to Lewisham or Deptford Bridge (see above). The airport is five miles from Goldsmiths.
From Luton Airport (LTN)
Shuttle buses connect the airport to Luton Station. Catch the Thameslink to London Bridge, then travel to New Cross or New Cross Gate Stations by main line train.
From Gatwick Airport (LGW)
Catch a London-bound train from the airport station to East Croydon Station. Change there and catch the train to New Cross Gate. The journey time is about one hour.