Accident damage

Hi,
I had an accident which was the other drivers fault, he did not stop at a junction and collided with my vehicle.
The damage to my vehicle although extensive is purely cosmetic. My car is still drivable.
My Insurance company has written my car off as the repairs will cost more than their vehicle valuation.

I would like to purchase the vehicle back and have the repairs done myself, as i feel the Insurance company have not done a true valuation. i.e. Full service history, condition of vehicle, milage etc.
I have always taken my car to Halfords Autocentre for any repairs needed to engine, brakes tyres etc and never used a cheap garage.
I use my car for work to carry my work things.
I am a self employed cleaner, so it essential that i get a vehicle/my vehicle back on the road as soon as possible.

I am confused as to weather i can still drive my car around as i have been told different things.
My legal team, acting solicitors, state that it is fine to drive. But i would like to know what the law is in these cases.

Also, if i buy back my car from the insurance company and have the work carried out myself do i have to have a new MOT issued? (There is no damage to any working parts, just bodywork).
If you can help answer any of these questions i would be grateful.