My insurance agent explained it thus.
As long as the car does not belong to you, you can drive it under 3rd party extention.
You cannot get out of the car until it is on private property, as as soon as you get out, the vehicle is no longer insured as you are no longer in control of it.

So, as said, if you are stopped by 'da filf', you can't get out. if you do the car is no longer insured, however, if you do get out and turn the engine off, you are no longer driving, and thus you cannot be driving an uninsured vehicle. as soon as you get back in, the car is insured again.

Weird or what??

There's two aspects to this discussion.
1/ is that each car on the road must be insured.
2/ is that every driver must be covered to drive it by a certificate of insurance.
So, My 3rd party extension covers me to drive it, and the owners insurance covers the cars legality on a road.
The only insurance that covers an uninsured vehicle is the type often taken out by businesses that insure "ANY" vehicle, not like the standard insurance which stipulates the exact car.
We could obtain this type of cover but it's extremely expensive and only really useful to mechanics and the like. Now, if mechanics could just use their 3rd party extension, they wouldn't need to pay extra for "Any vehicle" cover.
There, clear as mud!!!

Your right LiDLe, I wanted a definitive answer so I asked the Police National Legal Database who confirmed that if the insurance company have worded your cover correctly, your OK to drive on third party cover of your fully comp insurance.
I went one step further and asked the question raised by another member regarding Mr Plod inviting you out of the car to sit in his nice shiny police car. The following is the answer given:-

I appreciate you want it in black and white, but it will depend to a
certain degree on the actual terms of the insurance policy. In most
circumstances there won't be a problem, but it would be wise to check with
your insurance company. As to B if a police officer temporarily interrupts
your journey or you jump out and dive behind a bush because you have to
have a jimmy riddle, the courts have determined that you are still the
driver for that period.

So there you have it. I was wrong and I'm happy to have an official answer.

Uncle Buck