Depends on when the car was first used.
"According to the Construction and Use Regulations 1986, all vehicles must have at least two mirrors unless they were first used beforethe 1st of August 1978 (in which case one is sufficient).
If the rear-view mirror is obscured then a vehicle first used after the 1st of August 1978 must have both of its side mirrors intact. Failing that, the vehicle must have an undamaged rear-view mirror in place, and a working driver’s wing mirror also. Mirrors which are intact must also be in a position which makes the road behind visible to the motorist.
A driver will be in danger of being stopped by police if they have no driver’s side mirror, as well as being at a higher risk of suffering personal injury in a crash or causing someone else harm due to having restricted view of their surroundings. A car without a driver’s side mirror will also fail an MOT.
If a vehicle has had its passenger side mirror broken off or its glass smashed in a way which makes it impossible to use, then a driver can still legally drive the car without it. "