Has anyone ever experienced having a hand brake mount snap off ? If so how do we fix it ?

Are you talking the handbrake lever from the floor , if so been there done that , I drilled a couple of hole's where the spot welds had been and used short bolts with nyloc nuts . If it's not there then disregard this answer .....

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Morris 1100s with bench seats have the handbrake between the seat and the door.

I have had two handbrakes crack and ultimately break. I bought one from a british heritage wrecker and it arrived having being repaired by welding. The next one that split I simply had welded.

Bottom line - If its metal it can be welded. !!!

The bit that broke is where the teeth of the hand brake lock thing bolt to the car the hand brake is in between the seats hence where the broken plate is do I have to make a new plate as the original looks pretty flimsy?