I used to do airport parking and then found it better just getting a hire car, I would usually find a good rate with Hertz for the week with no one way fee using my Amex Plat card or I would book a car with Thrifty since they had a branch 2 mins from my home and book a day rental. Would usually work out around £120 for the entire trip and usually I would book a three series or similar.

Other option as others have mentioned is Just Park, you are parking on someones drive but compared to some of the companies that pick up your car or leaving it in T5 you have a similar level of insurance ie for you to demonstrate who specifically caused the damage.