Generally cars aren't insured, it's drivers that are insured. This works out ok for an insurer, since if they cover a driver on multiple cars, the risk doesn't go up so much, since one can only drive one car at a time. I think insurers in the UK fairly commonly default to insuring a driver to drive any car as long as it isn't for profit or racing or being hired by the driver. Check with your insurer, if they dont' default to it they will probably cover you on request.
To expand on abfandango, its not actually correct that the driver is insured its the car. Yes policies do cover a driver to drive other cars but thats just an added bonus most do to get your buisness. The reason its on the car is that your insuring your car (90% of the time) for fire and theft and no insurance company is going to insure loads of cars on the same ploicy for that reason. So in summary you may be able to drive both cars on the same insurance but both cars are not insured, only one. You can get a policy to insure more than one car but it would be more money due to the theft/fire implications but not as much as the 2 seperatly. So to answer the question, you can have as many insurance policies as you like.
I am with Endsleigh and recently I was in the same situation. I was in possesion of 2 cars. When i called them up they added the extra car on to my regular policy for a cost of �42 a month( it was a knackerd Carlton so it may be more for a new car) . So, yes it is possible and extremely hassle free.
Rang my insurer yesterday and they have changed my policy to the new car (charge: �25) and put my old car on temporary cover for 30 days (�50). Just in case anyone wanted to know the outcome!