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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.
You replied as I was typing ^. All police ARV crews are given this training, I doubt very much that the military were involved on the ground.