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I agree it is unlikely that the military fired the shots but I think it is possible.
Firstly, it has been confirmed that the SAS were deployed on the ground to hunt for a suspected fourth terrorist. They were dropped off on London Bridge by an unmarked civilian registered helicopter. There are several mobile videos online showing non standard dressed military personnel with balaclavas rapidly moving through the area. I assume this was them.
There is footage of military personnel on the ground in standard uniforms although I assume they weren't part of a rapid reaction force.
I believe that if you are firing at somebody wearing a suicide vest, the training is to put as many rounds into them as possible in order to disrupt the nervous system enough to prevent a trigger being pulled. It would be unusual to be dealing with an explosive that could be impact triggered.
I have a hunch that it may not have been police that fired at the terrorists. It all smells a bit military to me.