It could force the Government to call in troops to carry out day-to-day guarding and patrolling duties at major transport hubs, city centres and key buildings such as the Houses of Parliament, he suggested.
Mr White, who opens the federation’s annual conference in Bournemouth, Dorset, on Monday, said a national shortage of armed police was leaving Britain vulnerable to terror attack.
“I think there is a real possibility the Army could have to be called in to conduct routine duties that are currently performed by authorised firearms officers,” said Mr White.
“If you cannot get police officers carrying guns then you are going to have to have the Army on the streets.”
Mr White’s comments come just days after the threat from Northern Ireland-related terrorism in Britain was raised from moderate to substantial.
The Government has announced plans to recruit 1,500 extra firearms officers in the wake of the Paris and Brussels terror attacks.
But there are already at least 300 vacancies across England and Wales as numbers of authorised officers have fallen to the lowest level for seven years.
Mr White said: “Before we even start talking about recruiting the extra 1,500, we are struggling to fill the vacancies we have currently got because of the lack of understanding and protection that officers would have if they have to discharge their firearm.
“That’s what this survey says – we do fear violence, but officers don’t want to carry firearms because they are concerned that if they discharge it, they are going to get arrested for murder.”