Don't know about Leytonstone, but the Lee Rigby killings was not for a lack of mechanisms, the jihadis who beheaded Lee did so because he was in military uniform and they wanted to kill a soldier. They even had friendly conversations with the infidels around them whilst their hands were covered in blood. Adebolajo and Adebowale had guns on them, which they tried to use on the police, the police won that fight. This is in contrast with say Paris, where their focus is maximizing casualties for maximum impact
Most of that is true but I'd point out that they only had one gun and it was a 90-year-old revolver that failed to fire a single shot because it was a rusty piece of shit. I think that counters the argument that terrorists will always have access to the best weapons even if you restrict them (and the perpetrators of the Woolwich attack had a far more direct link to terrorists than Mateen has seemed to so far).