It depends on the damage as to whether it would fail the MOT or not. If any jagged metal is sticking out and could be dangerous to people getting in, out, or then it will fail. If it's just a 'crease' in the metal, then it should be absolutely fine.

The MOT test states that a reason for failure would be "A sharp edge or projection, caused by corrosion or damage, which renders the vehicle dangerous to other road users, including pedestrians"

Isn't there something that says the door musr be capable of being opened from either side ?

Yes, there is. But the OP has stated that the door is working from both sides.