Please note this question applies to car insurance in the UK (but all advice is welcome!)

I have a standard insurance policy which includes Social, Domestic, Pleasure and Commuting and is fully comprehensive. My job will now however require me to attend meetings at various client sites, obviously during work hours. Does this mean I have to extend my policy to cover Business use as well? If so should I my employer reimburse this (in addition to the 40p per mile they will pay me)?

A few details:

I will ONLY use the car to travel to client sites. I will not transport equipment (apart from a laptop) or do any deliveries etc.
It’s my own car and I am a NAMED DRIVER on the policy (i.e. not the policy holder).
I will only travel once or at most twice a month to meetings.
I have two cars insured on the same policy (if this makes any difference).

I would really appreciate any advice you can give me on getting the best deal (in case I DO need to get extra cover).