Lawyers could argue over such cases for hours (or, more likely, weeks!).
However, while the Highway Code isn't a statement of the law, it can be used as a guide by courts when assessing whether someone was driving responsibly. Rule 201 states "Do not reverse from a side road into a main road. When using a driveway, reverse in and drive out if you can."
The woman who was reversing out of the drive was clearly at fault for putting herself into a position where it was necessary to do so. (She should have reversed in). Once she'd got herself into such a position, she should have been checking BOTH directions for traffic crossing her path (where 'traffic' includes, for example, pedestrians and kids on their bikes).
The driver who was reversing along the road should also have been watching for vehicles pulling out of driveways (irrespective of whether they were reversing or not) but he/she certainly wasn't wholly at fault.
Further, a claim for non-existent whiplash injuries is an offence under the Fraud Act 2006, carrying a potential penalty of up to 10 years imprisonment.
Chris