I have rented through Enterprise at LHR several times and been happy with them. What I do is book the rental through their UK website which provides more information. Their listed price on the UK website includes the damage waiver which you can decline if you have personal insurance.
https://www.enterprise.co.uk/en/home.html
I believe it also helps to be part of the rental company's loyalty plan. I'm an Enterprise Plus member and had a small dent overlooked when bringing a car back to LHR.
The other advice is know how to drive a stick or be prepared to pay a much higher daily rental rate.