John Apter, head of the Hampshire branch, told the BBC that a national shortage of armed officers could leave police in isolated areas “unarmed and vulnerable”.
After the terror attacks in Brussels, the Government announced more firearms officers would be trained. But in Yorkshire, it is claimed that police in rural parts of the region no longer have the resources to quick respond to incidents like the 2010 shootings in nearby Cumbria, where Derrick Bird killed 12 people.
Speaking to BBC Radio 4’s File on 4, Mr Apter said that there were potential targets in rural and coastal areas - such as energy and power plants - but that armed officers could be more than 70 miles away in an emergency.
“Being realistic, if a firearms unit was coming from the middle of the county you are still talking about 30 miles away - you are not talking about a few minutes,” he said.
He said the distance would mean an understandable delay which would be even greater if the officers had to come from as far away as 70 miles.
“So the only officers that you have available are unarmed and vulnerable officers and they are the officers that are saying to me that in a terrorist situation they would be sitting ducks,” he added.
His concerns come after new figures released last month showed that the number of firearms officers in England and Wales plunged by nearly a fifth in five years.
Earlier in April Prime Minister David Cameron announced that more armed officers were to be stationed across the country to deal with a Paris-style attack.
Forces are training around 1,500 extra personnel as part of counter-terrorism efforts, with 400 ready to be deployed to cities outside London around the clock.
Police minister Mike Penning told the BBC that £143 million had been committed over the next five years to provide “a national uplift in armed policing capability”.
Mike Pannett, a former North Yorkshire Police officer who ran as an independent candidate for police and crime commissioner, said the county was reliant on neighbouring forces in West Yorkshire and Cleveland for firearms officers.
Figures released recently by the Home Office show the force had 63 armed officers in March 2015 - the same number as in 2009 - a drop of 17 per cent on 2014, and down from 77 in 2012.
According to the county’s crime commissioner, it now has 77 officers attached to its specialist Firearms Support Unit.
West Yorkshire had 128 authorised firearms officers, South Yorkshire 86 and Humberside 79. The total for Yorkshire’s four forces, which stood at 356 last year, is down from 408 in March 2012.
Mike Stubbs, Chair of North Yorkshire Police Federation, said: “This issue isn’t just about terrorism. Many people will remember the horrific events in Cumbria in 2010 when Derrick Bird killed 12 people. Cumbria and North Yorkshire share many similarities in terms of their vast geography and rural nature.
“The same challenges that Cumbria Police faced in responding to that incident would apply to a similar incident here, whether it was terrorist-related or not.
“Without the routine arming of all police officers, there would have to be a significant increase in the number of armed officers to ensure that an incident of that nature could always be responded to quickly, anywhere across the 3,000 square miles that our officers police.
“We did not have those resources before the Government slashed police budgets - we certainly do not have them now.
He added: “While some may question the likelihood of an act of terrorism occurring here, this does highlight the risks that police officers in rural areas face on a day-to-day basis, when assistance can be a considerable distance away.
“We have been working with our force to review the number of taser-trained officers and look at where they are deployed.
“The Police Federation have been calling for some time for Taser to be available to all operational officers who wish to carry it.
“Sadly, at our national Conference today, the Home Secretary gave no encouragement that the Government was willing to provide Chief Officers with the resources to enable this to happen.”
Julia Mulligan, police and crime commissioner for North Yorkshire, said: “North Yorkshire is the safest place in England and thankfully firearms incidents happen only very rarely.
“However, the Government decided more armed officers were needed following the terrorist attacks in Paris and Brussels. How many are needed in an area is dependent on local risk assessments which take into account the local geography – including whether the force covers a wide rural area.
“North Yorkshire Police currently has 77 officers attached to its Firearms Support Unit which is specialist team of highly trained police officers who volunteer to carry out this highly responsible role in keeping the public safe.”
Mr Pannett said recent high-profile and long-lasting investigations into the actions of firearms officers was putting existing officers off from applying to for one of the 1,500 new roles.
He said: “It is all very well announcing an additional 1,500 cops, but people are not willing to volunteer to become firearms officers.”
He added: “People might say ‘why would anyone want to attack North Yorkshire’, but we have the second-busiest tourist destination in the country in York. We have York, Harrogate and Scarborough, we have York Minster, we have the biggest Army barracks in Europe.
“If you look at what happened at York at the weekend, there were 30,000 people packed together for York races, how many people have we got in the area of the racecourse, the answer is none.
“With the additional 1,500 officers to train up, how many are North Yorkshire getting? They are already struggling with numbers.”
He wrote in a column for The Yorkshire Post in February: “Northern cities have been targeted by terrorists in the past – they’ve even focused on small towns – so where do the likes of York, Harrogate and Skipton fit into the larger picture? How capable are they responding to a terrorist incident?
“Several chief constables from the North have now spoken out, one or two quite candidly, and they’ve said that they simply couldn’t cope. They’d probably manage to get a handful of armed response officers to the scene within 15 or 20 minutes in a big city like Leeds. But in York? Or a rural market town?
“Our neighbours in West and South Yorkshire, and Humberside would rush armed officers to our assistance, as we would for them, but inevitably it would take time – and overlooks the fact that they might be dealing with an attack themselves.”