Getting from L. Heathrow to L.Gatwick

Personally I would want longer than 3.5 hours for this transfer. I would want over 4 and preferably more like 5-6 hours.

At the best of times it's about an hour's drive between the two but the route is on the busiest motorway in Europe. So any trip at rush hour or if there is any sort of accident on the route and it will be significantly longer. The coach transfers are generally scheduled to take about 90 minutes but again can be delayed by traffic.

You can take a train into London and out again - Elizabeth Line to Farringdon and then Thameslink to Gatwick. That will take 90-105 minutes but it's probably a bit more reliable on time.

Then you have to add the time getting out of Heathrow, through immigration and maybe collecting bags and then checking in ahgain at Gatwick. Don't forget that you will probably need an ETA as well.

Have you already made those flight reservations? I'm seeing red flags all over the place, depending on where your first flight is coming from and whether these flights are on one ticket or 2. Certainly possible if your first flight is from inside the UK, and it arrives on time, and you dont have checked luggage to pick up, and your car service is waiting for you, and there are no traffic disruptions on the drive and you already have your boarding pass for your outgoing flight and you dont have to check luggage, and there are no long lines for security, and there are no long lines for Passport Control, and you can reach your gate before it closes 30 min before your departure time. In those circumstances a car service would work. Black Cabs is often recommended. Note that Gatwick airport recommends that passengers arrive 3 hours before departure. It is not physically possible to arrive in Heathrow and get to Gatwick in 30 minutes.