"in simple terms how the heck did it do that?"
as you've probably worked out "simple" and airborne gravity" can't be used in the same article................ They normally measure the gradient and it's variation
https://en.wikipedia.org/wiki/Gravity_gradiometry is a reasonable start.
As for Oil & gas in the Weald there are several producing fields - mainly to the south side of the basin but the current operation at Horse Hill is very close to Gatwick and that has just received planning approval for 2-3000 barrels a day for 20 years.