(There used to be an excellent police blogger who talked about doing this from firsthand experience, but he was de-anonymised and his blog taken down).
As a former UK police officer I can assure you that if armed police officers came across someone with a drawn knife at least one firearm would be aimed at them.
One of my officer safety trainers was a qualified close protection officer (i.e. bodygaurd) who ran through one of their scenarios whereby someone with a knife faces off across the diagonal length of a basketball court sized room with someone with a holstered gun. Even trained officers can't reliably get a shot off if that person starts sprinting towards them.
Believe me no-one wants to try and tackle a knife wielding suspect with a baton, at that point you're using defensive tactics and your partner will use their CS/PAVA to try and disable them.
Fortunately, in the UK, the vast majority of people with knives aren't actively homicidal at the point at which the police turn up.
Nightjack was amazing, the Times is in my permanent bad books for their nonsensical justification for outing him. He thoroughly deserved the Orwell prize that he won for his blogging.
I can remember the proper name for them but it's along the line of Armed Emergency Response Teams. Watching tapes and a short training exercise the amount of trigger discipline and weapons handling is amazing.
Armed Response Vehicles (ARVs) are the mainstay of British armed policing, outside of London they are pretty rare and often fall back to traffic policing duties.
The qualfiied officers are Authorised Firearms Officers who will also stand up the equivalent of SWAT teams as needed for each constabulary.
London has Specialist Firearms Officers as well who are a standing set of SWAT type teams. Several have written some very good books about their experiences, Steve Collins especially.
The main thing in the UK is that armed officers who discharge their weapon, let alone kill someone, face extremely rigorous scrutiny by an external agency. This combined with no specific legal protections means that a police officer shooting their weapon is very rare, it happens a handful of times across the UK each year.
I think I helps when the odds are low that suspects will be carrying firearms. In north America the odds are much higher that police will have a confrontation with armed suspects --and of course NaM police have greater legal protection when discharging a weapon.
Believe me no-one wants to try and tackle a knife wielding suspect with a baton, at that point you're using defensive tactics and your partner will use their CS/PAVA to try and disable them.
Fortunately, in the UK, the vast majority of people with knives aren't actively homicidal at the point at which the police turn up.
Nightjack was amazing, the Times is in my permanent bad books for their nonsensical justification for outing him. He thoroughly deserved the Orwell prize that he won for his blogging.