Can an employer require employees to provide proof of car insurance when not driving a company car?

If you are using the car for company business - i.e. traveling in it while AT work (not going to and from work in the morning/night), then not only can they ask you for proof of insurance, the MUST ask you for this.

If you are driving the car when working for them and you then have an accident, they could be sued if you are not insured and further, the police could hold them criminallyliable.