Ask MID - CGNorwich
Just renewed my insurance and checked that showing on MID.

Notice that there is also a facility on the site to check third party registration numbers if involved in accident. You need to pay £3.50 and you will receive on screen the insurance details: policy number, name of insurer and the claims contact details to help you progress a claim.

Don't recall this was there last time I looked
Ask MID - Rattle
It has always been there, but the website has been redesigned and it is a lot more obvious now.
Ask MID - Galaxy
The last time that I was unfortunate enough to be involved in an accident, I got all that information from my own insurance company for free when I reported the event.

No need to pay £3.50 to Askmid for the same thing!