Blimey there is some bad advice amongst these answers!
The cover you are looking for is generally called a 'driving other vehicles' extension. It does not matter whether you are third party or fully comp, typically if you qualify you get the cover.
Normal criteria for qualifying for the extension are age related (unusual to qualify if under 25) and occupation related (unusual to get it if in motor trade / driving trade).
The only way to know is check your certificate of insurance - Where it lists your reg number it will typically tell you if you have insurance to drive other cars. If unsure, call your company.
Just be wary then of the criteria for driving. The other car needs to be taxed, MOTd and insured in someone elses name and of course you have to have their permission. Plus remember if you damage the car, you have no ability to claim!
http://www.superquote.com - I have experience in UK personal finance, particulalry personal insurance