The registered keeper does not even need to have a driving licence, let alone have insurance for the car.
However the text of the relevant law is:
http://www.opsi.gov.uk/acts/acts1988/Uk ... tm#mdiv165
Quote:
165.—(1) Any of the following persons—
(a) a person driving a motor vehicle (other than an invalid carriage) on a road, or
(b) a person whom a constable has reasonable cause to believe to have been the driver of a motor vehicle (other than an invalid carriage) at a time when an accident occurred owing to its presence on a road, or
(c) a person whom a constable has reasonable cause to believe to have committed an offence in relation to the use on a road of a motor vehicle (other than an invalid carriage),
must, on being so required by a constable, give his name and address and the name and address of the owner of the vehicle and produce the following documents for examination. [...]
The question is whether they have reasonable cause, this is probably one to look up in Wilkinson's.
Finally, if they DO have insurance covering it then it would be safer to produce it and then complain that it was not a lawful request. If they DON'T have insurance then they can only say that they aren't insured for it. If they have been asked to produce the licence etc. then produce these, don't fail to produce just because the car isn't insured for that driver.
Finally (!) note that only a constable can request production of insurance - unless the letter is from a constable he can rightly tell them to "get stuffed", although it will probably only result in a letter straight back from a constable in the same office. (I think quite a few SCP's are making unlawful requests like this)