Take the Piccadilly line from central London straight to Heathrow; it’s affordable, frequent, and stops at all terminals

https://www.scribd.com/document/1074920514/Getting-to-Heathrow-from-Gatwick-Easiest-Inter-Airport-Transfers-178501

Take the Piccadilly line from central London straight to Heathrow; it’s affordable, frequent, and stops at all terminals, though it can be crowded during peak travel times.