I've always found the cheapest airport parking to be Holiday Extras via Moneysaving Expert.
https://www.moneysavingexpert.com/travel/cheap-airport-parking/#holidayextras
Doing that for Gatwick brings up some hotels I don't recognise, then Holiday Inn and Premier Inn. But I see that the transfer part seems to be payable on top and contracted out.
What about booking separately? Book Gatwick parking then the cheapest Travelodge/Premier Inn etc maybe half an hour from the airport if you don't want to be driving from home to the airport before the flight?