If you’re transferring from Heathrow, use the RailAir coach or Tube to Victoria, then train to Gatwick

https://www.scribd.com/document/1077066259/Heathrow-to-Gatwick-Airport-Transfers-Coach-Taxi-or-Train-174457

If you’re transferring from Heathrow, use the RailAir coach or Tube to Victoria, then train to Gatwick. Direct coaches also run between airports at certain times—book ahead.