From Croydon, hop on Southern or Thameslink from East Croydon station

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

From Croydon, hop on Southern or Thameslink from East Croydon station. Trains to Gatwick are frequent and fast, often taking less than 20 minutes platform to platform.