Police could be stripped of their role in leading the fight against terrorism and replaced by a national agency directly answerable to the home secretary, under advanced plans being studied by Theresa May.

The Guardian has learned that May’s officials have begun approaching senior candidates who could lead the review, whose key question will be whether the National Crime Agency (NCA) should take over from police.

The police are expected to vigorously resist the change and argue that the current system is the “most effective way of countering the threat” of terrorism.

Scotland Yard would view the loss of its lead role on terrorism as a humiliation. May will make a final decision on whether to go ahead with the review, to be undertaken by a panel of experts, early this year.

It could provoke a fresh clash between the Conservative home secretary and the police, as May’s supporters say she has been battling to reform and modernise the force.

The NCA, styled as Britain’s FBI, is directly answerable to the home secretary. It has been leading the fight against organised and serious crime since 2013.

Scotland Yard, based in London, leads on counter-terrorism operations for the police, with a series of regional units run by other forces contributing intelligence and making arrests. The security service MI5 is in charge of gaining and developing intelligence; its role and status is not in danger from the review.

The Home Office is looking for a high calibre candidate to lead the review and has approached the former MI5 director general Jonathan Evans, who declined due to existing commitments. Other senior candidates have been sounded out.

Police say the counter-terrorism hubs around the country, known as “the network”, are running at an intense level, making nearly one arrest a day.

May does not believe the current terrorism threat level of severe, which means an attack is highly likely, is a bar to examining the radical change, nor enacting it, if the review rules in favour of the NCA.

Time is running out for supporters of a shift of counter-terrorism responsibilities to the NCA, as such a move would need legislative time in parliament after the review publishes its report. Opposition from the police is expected.

The review was first delayed until after the 2012 London Olympics. It was further delayed while the NCA was established and ministers and senior officials waited to see how effectively it performed; whether it could “walk before it was asked to run”, as one put it.

In 2012 the government’s view that terrorism should be taken off the police and given to the NCA was so sufficiently advanced that a clause was included in a parliamentary bill, allowing the home secretary to make the change if she saw fit. In the meantime the influential, all-party home affairs committee backed giving the NCA the counter-terrorism lead.

However, a mixture of the terrorism threat level being raised in August 2014 to its second highest level, and the looming general election in May 2015, caused the idea to be shelved again.

In a 2014 Guardian interview the NCA director general, Keith Bristow, said he could see advantages if the government stripped Scotland Yard of its leadership of the fight against terrorism, as the capabilities and tactics in fighting organised criminals and terrorists are often the same.

Bristow, who stood down last month after a four-year term in which he oversaw the NCA’s launch, said: “The judgment that will need to be made is how do we get best effect out of our collective effort against terrorists and organised criminals … the strategic national threats that can’t be tackled in isolation.”

Supporters of the review say having the NCA in charge would bring national control and consistency to the counter-terrorism fight. Some in government fear that the current system, which critics see as ramshackle, might buckle under strain.

Scotland Yard defended the current system. “It is a model that has strong community connections, excellent relations with security and intelligence agencies, and can achieve global connectivity; is the most effective way of countering the threat from terrorism and protecting the public,” it said. “We believe the current counter-terrorism policing set-up demonstrates these elements.”

One police source said: “The idea of doors being kicked in by people dressed in black from central government may not go down well in certain parts of the country. It is different to doors being kicked in by local police, with contacts and connections to communities, who have legitimacy.”

But a Home Office spokesperson stressed the government’s record in providing the money to fight terrorism. “The first priority of government is to keep the public safe – that’s why we are taking all necessary steps to ensure our law enforcement and security and intelligence agencies have the powers, capabilities and resources they need.

“Since 2010, the government has undertaken significant work to strengthen our response to the threat from terrorism, including the protection of the counter-terrorism policing budget. We also confirmed in the spending review that counter-terrorism spending across government will be increased in real terms to invest in new capabilities.”