To find the warmest/sunniest resorts you obviously need to go south.
To minimise flight times you need to be looking for a destination which is almost due south of the UK (so that you don't waste time going east or west).
If you don't want to go as far as Africa (or the islands off the coast of Africa, such as Madeira or the Canary Islands), then an obvious choice would be the Algarve. Here's the weather in Albufeira in May:
https://www.accuweather.com/en/pt/albufeira/273200/may-weather/273200
The Algarve is served by Faro airport, with a multitude of budget airline flights available from across the UK (with easyJet, Jet2 and Ryanair). Flights from London take about 3 hours.
If that's too far away for you, then Provence is a possibility. (e.g. Marseille or Nice). Here's the weather for Marseilles:
https://www.accuweather.com/en/fr/marseille/170960/may-weather/170960
The flight time to Marseille (from Gatwick) is only around 2hours.
Anyone closer coastal resorts will be on the Atlantic coast, with possibly unreliable weather.
If you'd consider a city break though there are more options available to you, such as Bordeaux. (Weather:
https://www.accuweather.com/en/fr/bordeaux/131913/may-weather/131913 ). Bordeaux is stunning and just 1 hour 40 minutes from Gatwick.