Starting point for England trip

Assuming you are arriving after a long transatlantic flight, then it isn't a good idea to drive anywhere on your arrival day.

Where exactly do you want to visit? Southwest England to me means Cornwall, Devon and Dorset, all of which are c 3 hours + driving from Gatwick.

Brighton would be a good first base, close to Gatwick if you want to visit Lewes, Rye or Arundel.

Upon arrival you'll be sleepy, jet lagged, on unfamiliar roads, and driving on the "wrong" side of the road. Some are able to handle all that and be ok. Some are driving impaired without realizing it. And some shouldn't be allowed to handle sharp objects. Please consider staying somewhere the first night and then renting a car. Having even a small fender bender is not a good way to start any trip.

If there is a way to travel to your first destination by train, and then rent a car the next day, that's what I would recommend.

We just completed our 28 day drive tour of Wales and England last October.
It was great. We rented at Heathrow and drove to Bath (about 3 hours due to some road construction).

I didn't sleep much on the flight, but it did not affect my awareness on driving, even on the left. Of course, you have to judge for yourself how much driving you want to do after a flight from North America.

Gatwick is farther east than Heathrow and you would need to use mapquest to view potential routes. Also, if you are driving in rush hour traffic, that could be terrible on the M25 Orbital.

We didn't go the London or the SE of England on our tour.
You might consider going to Canterbury prior to going west.

We had been to Salisbury, Windsor Castle and Stonehenge on an earlier trip. That was nice. We stayed in Winchester on our recent 28 day trip prior to catching our cruise ship at Southampton for our trip back to the USA. Winchester is nice to visit as well.

Bath with the Roman Bath Museum is fantastic, but I would not use Bath as a home base.

We used Chipping Campden in the Cotswolds to visit almost all the towns and cities in the Cotswolds as well as Oxford, Blenheim Palace and Stratford Upon Avon. We stayed at the Volunteer Inn. Great at 80 pounds per night.

Here is my detailed trip report.
28 days in Britain and Celebrity Eclipse home
https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139

It really depends on which sights in the UK you’re visiting. Brighton and Bath are both good choices. If you were going to southeast England then I’d suggest Canterbury. Portsmouth is an option if you wanted to visit the old navy yard and HMS Victory. After a transatlantic flight I’m good to drive for 2-3 hours before I need to be off the road. Only you know how long you can safely drive after a long flight.

Thanks everyone for such great input. Knowing that we will be tired from the long flight from Canada we are thinking that we will only drive maybe as far as Brighton the first day then head west from there for the first few days.

Unless you are very used to driving on the left and you sleep during your flight you should consider taking a train to Brighton and picking up a rental car there the morning after your arrival day.

I would check distances/driving times on this site:>http://www.theaa.com/route-planner/index.jsp
Probably best to take a train from Gatwick Airport into Brighton on first day - rather than drive.

Check out on Google Maps > Gatwick Airport is just N of Crawley. (Live traffic flows on this map are at the time you click it).
https://www.google.co.uk/maps/@50.9484007,-0.2822134,47911m/data=!3m1!1e3!5m1!1e1

Also go to Streetview to see the places/roads.

gatwick airport has the train station just downstairs and frequent fast and efficient trains which whisk you to the centre of Brighton with nary a worry.

Get your car the next day.