I think we should have more armed response teams. But arming police officers won't stop police officers being shot.
It will however massively increase the numbers of people being shot, as police are only human and put people in f**k up situations with firearms, some will discharge these firearms in a bad way.
There is also the issue of the impact it might have on further alienating our various ghettoised populations of our major cities. to which police reengagement is a must. Visible police presences would help that, visible armed police presences would not. In a lot of cases the police are already viewed as an alien force outwith the community, arming them will make them look like an army of occupation.
Don't kid yourself, this is a massive problem and needs to be addressed. Part of what makes british 'policing by consent' so unique and in many ways so effective is that the constable is not simply a armed extension of the judiciary (as in many civil law systems, and murkia). He/she is effectively the community 'guard' a lot of the job is more social worker than anything else. This is how it should stay, and this is how it should be ramped up towards. Why? this is where a lot of the positive impact comes from, and other police forces around the world often struggle with it. Arming all police constables is to turn sharply in the other direction.
Furthermore, The whole quick reaction ART strategy generally works very well. Rare incidents like this do not change that. These women died doing their duty, but unfortunately this risk is part of the duty.