My mate had a similar situation - woman in a Merc pulled out of her parking spot on the street as my mate was driving past, didn't check if the road was clear and was on her mobile. The front right of her car smashed into the back passenger door of his, his sister was left with a huge bruise of her leg.
Initially she claimed responsibility (well, apologised and said "I just didn't see you", then "Well, you were going very fast") and swapped details, but when my mate phoned her later that evening to get it sorted, her husband answered and started denying responsibility.
Went through court, she even tried to claim emotional distress but it found in my mate's favour, with the judge actually shaking his head in a slightly disbelieving way. She changed her story three of four times - there was the original one at the scene, then the one her husband gave on the phone that evening, the one she gave her insurance company and the two different ones she gave my mate's insurance company. Fortunately her inability to get her story straight, combined with the photos of the scene (which disproved a couple of her versions) meant it was fairly obvious she was lying.
So, the good news is that you'll likely be fine, especially with reliable witnesses. The bad news is it took 2 years for my mate to get it sorted.