Have rented in Scotland (tiny roads), but not England, although there will be 5 of us together in Italy for a week in October. Everyone’s arriving by train, then splitting up after that week, so we won’t be toting around luggage in the car, and a compact will work.
Last year, just 2 of us - with luggage, got unexpectedly upgraded to a Ford Puma compact crossover/SUV. The covered hatch storage compartment held our 2 international carryon sized suitcases, plus 2 day bags. Could’ve held 3 suitcases, but not 4. We did have the back seat open to toss in jackets, umbrella, or to keep backpack handy. And having everything hidden in the back hatch, under the cover, was easy.
With a smallish SUV, maybe you could fit in 3 suitcases, and strap in the fourth inside the car, between the two people in the back seat. That might be acceptable, or too cumbersome. Still, I doubt you could keep everything out of sight if you parked for a while. Much bigger sedan or SUV with a sizeable trunk is probably needed, for 4 people and stowable luggage. Maybe minivan?
In Scotland, medium cars got on the tiny roads going both directions, but there wasn’t a lot of extra elbow room on the road. Don’t drive too far left, avoiding vehicles coming the opposite direction, to risk running off the edge. There were relatively big campers - many with Belgian and Italian license plates, and they had a tough time staying on their side of the center line -driving their personal vehicles from the “wrong” side of the front seat, and on the left side of the road. Huge is too big, but medium might be what you’ll want, at a minimum.