What happens is this.
The car is declared a total loss - dependent on the level of damage, the car can still be repairable, although not necessarily economically so - i.e. they valued your car at �3500, but repairs come to �4000, so it's cheaper to write it off.
Once settled, the car becomes ours, and we send it to a salvage agent who then pays us a percentage of the retail value.
The car then becomes the property of the salvage agent. They then auction the car (dependent on the level of damage), and either a member of the public, or a trader, then buys the salvage for spares or repair.
Once they purchase the car, it is generally at this point that the DVLA send you the letter - the insurance company will never register the car in their name, and the salvage company will just send the transer to the motor trade slip, which again won't trigger the DVLA letter.
Hopefully that should give you a bit of better insight into the insurance circle of life!