You are really asking about car services, not cabs. justairports.com may or may not work for you (since you aren't going to an airport).

Or google Ray Skinner - he has a good car service

There will be plenty of local minicab companies around Kew, or there are several numbers to call for a standard black cab:
http://www.tfl.gov.uk/tfl/gettingaround/findaride/default.aspx
http://www.tfl.gov.uk/gettingaround/taxisandminicabs/taxis/1136.aspx

Many thanks to both of you - how reassuring to have your answers so rapidly! Now off to the doctor to check out the knee damage. Di

Sorry about your knee.

www.addisonleigh.com

This firm is very reliable, clean cars. Somewhat less than a black cab.

Swiss Cottage Cars offers all services at super prices and is very reliable. I was even able to call them last minute one time when we arrived at the Underground station to find our line closed temporarily.
207-431-2700.

Cathinjoetown means http://www.addisonlee.com/

Swiss Cottage is quite a way from Kew - they might charge extra for getting there in the first place; still no harm in asking.

Swiss Cottage Cars is all over London, the cars do not necessarily come from Swiss Cottage. In fact when they answer they may answer with a different name as they have tons of drivers from all over.

Thanks, PatrickL

Thanks, everyone for all those suggestions - they will be handy for future reference.
The owner of the B&B we were staying at also knew of a very reasonable service that he'd used for other guests, so we went with them this time. I don't know the company name, but the phone number is 0208568666. Kew to St Pancras they charged £30. Di

Addison Lee
www.addisonlee.com