http://www.bbc.co.uk/news/10260298
And personally, I wouldn't be keen on the police being armed all the time - I suspect it would make them a lot less approachable.
As a law abiding American, I can confirm that statement. There are a lot of scary looking characters that you can see while strolling through my city but none of them make me as nervous as police officers.
[NB I'm in Edinburgh which is usually full of tourists so I suspect the police are particularly well behaved here!]
It's more things like this I'm talking about:
http://www.youtube.com/watch?v=fpjFsmTDWuQ
It's obviously an extreme example but it illustrates the point, as does that business on the white house lawn.
(Also I'd contend that in practice most knife-wielding assailants, far from being even moderately trained, are probably clueless and scared.)
I don't agree with shooting anyone who is brandishing a knife, but trying to disarm them is a horrible idea as well. As others have mentioned, using beanbag guns or a taser or tear gas or rubber bullets or just about any less-lethal option (with other officers ready to shoot if the assailant charges) is the best solution.
I once wanted to be a police officer, and went through police training in Florida. I also currently study Aikido and Kali (Eskrima). I have practiced many knife disarm techniques and some defensive/offensive knife use. Taking a knife from someone who is actively trying to hurt or kill you with it and has even minimal training in how to use it for that purpose is extremely difficult. You will almost certainly be cut, and a cut to the arm can disable your hand. A baton improves the odds, but it's still very risky. Most police body armor does not provide significant protection from knives, nor does it cover the arms, legs or neck, which are excellent targets for a knife.
Disarming or disabling a knife-wielding attacker requires tools that can be used from a long distance. Pepper spray and Tasers are good less-lethal options, especially when multiple officers are present. These should be tried in most situations before going to a firearm, but if a suspect charges an officer with a knife there isn't time to wait and see. The range of a Taser happens to be the same (21 feet) as the distance most people can cover in the amount of time it takes for most officers to draw and fire a pistol. If the Taser fails or misses, it doesn't hold a second shot and can't be reloaded quickly. Most of the time, I'd want the officer to risk trying the Taser, but it's not reasonable to ask someone to go up against a knife unarmed.