Firstly, car insurance history is shared by insurerers as a "closed user group", this means mortgage lennders don't see it. However if the insurance was on credit, the infomration may have been shared with one or more credit reference agency (Experian, Callcredit and Equifax).
You can get a copy of your file and check what's recorded.
Generally, other people's information is not considered with yours unless there is a financial association. If you have had joint accounts or applied for credit in joint names with your girlfriend, there will be an "association" link on file. You will discover this when you obtain a copy of your file. If there is no longer a link between you, you can notify the credit bureau and they will remove it (unless there is evidence to the contrary).
So, in a nutshell, an ex's performance should not impact your credit score or credit rating. Phew