Police will not be able to enforce all the rules of the coronavirus “lockdown” imposed by the prime minister, a senior officer has said.

John Apter, chair of the Police Federation of England and Wales, said it was “not realistic” for officers to check how many times people had exercised in a day.

“Certainly the police will get involved with more than two people gathering in the same place, but as far as policing the bread aisles in the supermarkets, or checking how many times people are going to the shops, that’s simply impractical,” he told BBC News.

Mr Apter appealed for the public to heed the government’s advice to avoid putting further pressure on police as they try to support the NHS.

He said local authorities would take the lead on shutting down non-essential shops that refuse to close.

“The biggest concern is how we enforce social distancing,” Mr Apter added. “We police by consent and I don’t want that to change during this crisis… this is about saving lives and protecting people across this country.”

There was confusion over how the new rules would be enforced following Boris Johnson’s announcement on Monday evening, with the chief constable of Northamptonshire Police saying its phone lines were “crippled”.

Lincolnshire Police warned of an “extremely high volume” of calls, and Humberside received “a number of calls” on the subject, but the chief constable admitted they were unable to answer the questions asked.

Martin Hewitt, chair of the National Police Chiefs’ Council (NPCC), told BBC Radio 4’s Today programme, that the legislation necessary to enforce the lockdown has not yet been enacted.

He said the interim time was an “opportunity” for police to speak to people to urge them to go back home, but added: “Ultimately, if people do refuse to abide by the rules then we will need to enforce them.”

Asked whether it was the police’s role to be at railway stations to check if people should be getting on to trains, Mr Hewitt said: “I don’t think we’re at that stage at the moment.

“I think the real point about that is really getting the clarity, I know some other people have said that this morning.

“These are new rules, they are trying to be as clear as they can, but it will take a while, I think, for everybody to get that understanding.”

In an address to the nation, Mr Johnson announced that people would only be able to leave home to shop infrequently for basic necessities, for one form of exercise a day, medical needs, to provide care, help a vulnerable person or go to work if “absolutely necessary”.

Mr Johnson said all shops selling non-essential goods would be shut, as well as leisure premises and places of worship, with “all gatherings of more than two people in public” banned.

“If you don’t follow the rules, the police will have the powers to enforce them, including through fines and dispersing gatherings,” he added.

The military are expected to be called on to take on some police roles, such as guarding nuclear power stations, but not to enforce the lockdown.

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The Police Federation, which represents 120,000 rank-and-file officers, said it would not be “business as usual” for policing.

Police leaders have already admitted that a “graduated withdrawal of service” will be enacted if the coronavirus epidemic continues to worsen, with emergency response and threats to life prioritised over proactive patrols and other functions.

Research by the Policy Exchange think tank said the changes could drive localised spikes in violence if gang members feel “immune” as they complete over a shrinking drugs market.

The NPCC has asked for voluntary special constables to be released from their jobs and are relaxing rules on officers rejoining the service after retirement to bolster ranks.