If the car is currently taxed you can retax from the 5th of the month before.
If it is sorned I think it is either 2 or 5 days before the end of the month so it starts in the next month.
The only cheats I know are to either use trade plates or to book, and it has to be a pre-arranged booking, for an MOT at a garage just the otherside of where you are taking the car, an insured car can be driven to an MOT even if it has no tax or MOT.
Make sure that the car is insured, your fully comp insurance will cover you to drive other cars THAT are insured by someone else. Your policy wont cover you for a car that has no insurance on it.
Home to black Alfa Romeo 159 3.2 V6 Q4 ,green MGF VVC and red MG Maestro T16.
MG - the friendly marque.