The Queen used to drive around their estate lands all the time in a Land Rover, but even though she is younger than her husband, I don't think she drives at all anymore.
The vehicle the Queen liked to drive was a Jaguar X-type, the wagon (’estate’) version. She drove it herself within the past few years, but I think she has given up driving now.
The Queen likes cars, and was known to drive around estates in an older base-version Land Rover, maybe a Defender.
The Prince was driving an LR Freelander, which was sold in the US as the LR2.
All three of the vehicles are entry-level, not the top-end models that might be expected.