This information is for travelling to Yarnfield Park, which (obviously) we are not doing in 2021. However, we'll leave it here in case people are considering the 2022 MathsJam.
Gatwick is very similar to Heathrow, with tickets about £80 to £90.
From Gatwick what you probably want to do is take a train to London St Pancras, walk down the road to London Euston, and specifically buy a West Midlands Trains ticket from there to Stone. This will probably cost dramatically less than buying a ticket from Gatwick to Stone.
The Gatwick Express is generally not worth the extra cost, especially not if where you want to be next is Stone.
Another possibility is to take a train to Reading and then to Stone, which allows one to avoid London.
For options other than Gatwick see the page on Travelling by Air
Next: Travelling by train