Dayinsure operate on what is called a Difference in Conditions/Difference in Limits basis (DIC/DIL). Their policy basically has a clause in it which says that is there is another policy on a car, which would pay out for a loss, then their policy would not. Therefore there is not two insurance policies covering the same car.
It also says that any losses would be paid to the registered owner of the vehicle, thus getting round the issue of insuring a car which does not belong to you.
The idea behind it is quite effective really, and would solve the OP issue, although I would still think that in most cases adding yourself to the insurance on the car would be better.
Edit - just re-reading the original post, you cannot add the car to your normal insurance, but this specialist policy would cover you should you not be able to be added.