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Heathrow to Gatwick transport options: a pictorial guide
This guide is for people transferring between Heathrow and Gatwick airports.

For quick and easy: take the taxi.
For cheaper and still fairly quick: take the National Express
For cheap: use the Piccadilly line to Victoria (or Blackfriars) via Barons Court
Or the newest rail alternative: Elizabeth line to Farringdon followed by Thameslink to Gatwick.

Minimum connection time on through tickets is 3 hours. On the ground you need at least 90 minutes to make the connection, using a taxi. If you are late, then a delay taking you to 2 hours 30 minutes for the connection should still be do-able on most of the options listed here.

Details on contactless payment here, this will allow you to avoid queuing for tickets. This works on the Heathrow Express but buying in advance via their website and App is cheaper, with fares under £6 single if booked more than 3 months ahead.