Girona airport is a one hour drive from Barcelona and 30 minutes drive to the coast of the Costa Brava. Currently there are no flights from Gatwick to Girona.
To keep up to date on all the airlines that are adding Girona airport to their list of destinations, go to the official Spanish Airports page and select Girona airport.
You can also check the Gatwick airport destinations page:
If you wish to fly from London you will therefore need to consider either Stanstead or Luton airport which are services by RyanAir to Girona.
Girona airport is an alternative to Barcelona airport that also offers you easy access by road to both the coast of the Costa Brava and to Barcelona. Bear in mind that if you're flying to Girona to visit Barcelona then you have around a 1 hour 20 minute transfer time to Barcelona centre from Girona Airport if travelling by bus.