No, the system is okay as it is.
Armed response teams are picked for their temperament and good judgement and are very well trained.
You are asking a not so well trained officer, who may or may not be of such sound judgement and temperament to make an instant decision and act as judge, jury and executioner. This would probably lead to more UK citizens being injured or killed by the police, even with the best of intentions.
A surprise attack is exactly that and you are probably injured or dead before you have time to react with gun, tazer or pepper spray.
We are losing control in many of our cities like they did in the US, zero tolerance solved that. We know how to fix the problem, but there is no will to this where it matters.
I think the police are let down by the judicial system, with the criminal is treated as the victim and rehabilitation rather than punishment is all too often given as a sentence. A life sentence these days is a joke as it usually means 7 to 12 years inside. Life should be life, which we were promised when the death sentence was repealed. This would save an average of 3 lives a year, where a lifer has been released and goes on to kill again (according to Norman Tebbit in DT).
Unfortunately, it is going to have to get as bad or worse than the US was at its crime peak, before it gets any better.
Very sad what has happened in Manchester and I give my condolences to the murdered PC's families, friends and colleagues.

Is there a case for very violent criminals being held for a longer periods of time in custody, while an investigation proceeds, rather than them being let out on police bail? Checks could be build into the system, so the time period could only be extended by the judiciary etc. This is how the terrorism act works and when somebody is using a gun and in this case grenades, surely the danger to the public is of the same order of magnitude.