One problem related to car accelerates on its own has been reported for the 2007 Land Rover LR3. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2007 Land Rover LR3 based on all problems reported for the 2007 LR3.
I was pulling into a staples store parking space and went to stop. The Lr3 accelerated as I was braking and the powerful engine revved & wanted to keep driving the Lr3 forward. I kept my foot on the brake and immediateley shifted the Lr3 into park; shifted back & forth before the Lr3 stopped idle. Luckily there were no people or cars directly in front of me, but I did go across the lane and nearly hit a parked car. I am so concerned that I drove directly to the library; talked to a friend who said it sounded like "sudden acceleration", so I googled "2007 Lr3 sudden accleration"; this issue is on Land Rover forums, but there is no consistant definitive cause/solution to the issue. Filing a complaint with NHTSA and calling the mechanic tomorrow.