You could try your local MOT station to see if they would do a collection for the MOT.
There are some that do this. I did a quick google and found one.
Most of the other results were for scrap car collection and MOT failures.
If your car is already insured and your friend is also insured under another (their own) policy then they may be able to drive your car under Third Party cover. You could speak to your insurance about this.
The basics are that the car must be insured and the driver must be insured either on the same or separate insurances.
HTH
Sparky.