All rank-and-file police officers should be armed with a Taser because of the heightened security threat, the head of the Police Federation has said.
Steve White, chairman of the body which represents front-line officers, said acts of terrorism could be carried out anywhere and police needed to be protected.
He cited the killing of Fusilier Lee Rigby near Woolwich Barracks in 2013 as an example of how lone wolf-style attacks could be carried out without guns.
He told the Guardian: "The terrorist ideal to get attention no longer relies on an attack being in a place of note. It could be in Cheam high street, in any town, in any part of the UK. We know there are more dangerous people out there, preparing to attack police officers and we need to be able to respond to that threat.
"As (the) Lee Rigby (murder) demonstrated, you don't need to have a gun to create terrorism. It is a defensive tool and a tactical option. We have a largely unarmed service and the service wants that to remain.
"The alternative is to have officers out there without anything at all. We have to do something.The sector threat (to police) has gone up by two levels and we need to make sure everything is done to protect officers who protect the public."
The federation is to vote on the proposal next month, the newspaper said.
Home Office figures released last October showed the use of Tasers by police had increased every year, while there have been a number of controversial deaths related to the stun guns.
The weapons were fired 826 times out of the 5,107 occasions they were deployed between January and June 2014, with the latter figure compared with 4,999 times during the same period in 2013 and 1,297 times in 2009
Tasers were also pressed against a person's body - like an electric cattle prod, in what is known as "angled drive stun" - on 123 occasions in England and Wales in the same period.
Concerns over their use were heightened after the death of Andrew Pimlott, who suffered fatal burns when he was hit by the stun gun in Plymouth in April 2013, after he had poured petrol over himself and was holding a lit match at the time.
Amnesty International UK's arms programme director Oliver Sprague said: "We'd ask the question: where's the evidence that a terrorist will be deterred by the knowledge that police officers have Tasers at their disposal?
"And who on earth thinks that if there's a real instance of terrorist activity that Tasers would ever actually be sufficient for our law-enforcement officers?
"We've always said that Tasers can have a part to play in policing operations where there's a clear risk of death or serious injury to police officers or members of the public - but Tasers should be used sparingly and only by highly-trained officers.
"The real worry is that we'll actually end up with trigger-happy, under-trained police officers using Tasers wholly inappropriately against ordinary members of the public."
Commander Neil Basu of the Association of Chief Police Officers said: "The UK police service has introduced the use of Taser into mainstream operational policing with great care, listening to and understanding the concerns people have raised. Amongst those are officers themselves.
"Whilst I would support an extended roll out this must be informed by appropriate assessments of existing threat and risk, the high standards of training must not be diluted and they should only be carried by those who volunteer to do so.
"Taser is one of many tools and tactics available to help manage threat and risk which is continually assessed.
"The variety of force demographics and the threats faced don't always make it the first or most viable solution. It is for each chief constable to decide the appropriate number of Taser trained officers in their force based on the threat and risk they face.
"We take the threat to our own officers and staff extremely seriously and will continue to consider all options available to enhance their security. All our men and women on the frontline are used to confronting risk and danger and are well trained in how to protect both the public and themselves."