Two videos are not proof that the UK doesn't need all officers to be equipped and on the first video they didn't actually use a tazer, the mere threat of one got the guy to give up. I think you're overestimating how many guns are in the UK, yes - there is a problem in some parts of the country concerning illegal firearms but weapons are not as widespread and easily accessible as they are in America, knife crime is actually one of the biggest culprits over here at the moment.
We do have permantly armed officers like the ones you've posted in areas such as airports and Government buildings and each force will have a number of trained firearms officers throughout their jurisdiction that can respond at a moments notice (Armed officers responded to and dealt with the London Bridge attack within minutes https://www.theguardian.com/uk-news/2017/jun/04/police-praised-for-stopping-london-bridge-attack-in-eight-minutes) . The need is just not there at the moment to arm every officer, not to mention the UK Government keeps cutting back on the police, reducing their numbers - there's no way they could afford basic handguns at the moment
"Armed officers open fire rarely. In the eight years to March 2016 police discharged their guns during just 40 incidents. Since 1990, 67 people have been killed in police shootings in England and Wales." - https://www.economist.com/britain/2017/06/29/is-it-time-for-britains-unarmed-police-to-be-given-guns
One day in the future, yes we may need to follow in the footsteps of the US and other countries, but for now it is not necessary - to act as if producing a gun will solve anything is nonsense, it would not have stopped this attack as this guy was a traffic warden - they are not police officers.