Michelle,
There's a clear distinction between registered keeper and actual owner of vehicle and if you say that your dad has transferred ownership to your mum, it means that your mum has legal rights to the car now, that is, the car belongs to her by law. However this doesn't change anything as far as car insurance is concerned. If your mum is still a named driver on that policy and your dad the policyholder, then your dad will probably lose part or all of his no claims bonus (NCB) depending how much he's got if they were at fault.
In some very rare cases where the application form for the car insurance quote required confirmation of who was the car owner, the insurance company may cause problems if you didn't inform them when ownership of the car was transferred.
