The reason why so many cars are uninsured is because the owners cannot afford the very high cost of insurance, particularly young drivers who can face a premium of several thousand pounds a year. If the car is impounded it has to be reclaimed within seven days of the date it was seized, and taken away by the 14th day after seizure, otherwise it is confiscated.
A temporary policy could help you get your car back so that you could SORN it, sell it or save up for a yearly policy. The mimimum length of such a policy that will be acceptable by the police is 30 days.