When this happened to me i bought the whole glass+plastic backing for £22 from ECP.
Use the electric mirros to turn the mirror towards the car and the put a screwdriver between the back of the black plastic and your mirror casing.
(I put a cloth of some description between the screwdriver and the casing to prevent damage)
Then gently push the black plastic away from the casing and it should pop out, then replace with the new glass/plastic by just clipping back it.
Job done