You need a letter from your insurer stating that you would have been covered if you were involved in an accident with your car insured through them with an incorrect reg number, or it'll be classed as you were driving without insurance because the certificate/policy is wrong. Nasty but true, you weren't insured if it wasn't correct (there are lots of people every year don't get payouts because there is an error of the reg number or car type 'an IS not an SI' for example)

I've driven uninsured for a week, totally unaware, I phoned to add me to my partners policy and whoever I spoke to didn't put it through properly, when no paperwork arrived a week later I called them and found out. It was investigated and call records proved I was right and they'd have had to pay out if I'd had an accident, but if I had I wonder if that recording would have gone missing to save them ££ ?