The businessmen are also challenging the Executive on its decision-making process that led to the regulations coming into force.
The barbers include Sean Lawlor of Cambridge Barbershop, Andrew Kavanagh of Camlough Barbers, David Lutton of The Corner Barbershop, and Padraig McShane of Cut N Edge.
The Northern Ireland Executive announced that close-contact services, such as hairdressers and beauticians, were among a range of businesses required to close until November 13th.
Solicitors representing the barbers have asked to see evidence used by ministers to decide to close down those parts of the economy.
In a letter sent to the Executive, the group raised concern about scientific material that was published last week.
A scientific paper that guided the Executive’s recent decisions on the introduction of the circuit-break, estimated the closure of hairdressers and beauticians could reduce the virus’s reproduction number (R number) by 0.05.
The paper was published as part of an initiative by the Department of Health to increase transparency around the decision-making process.
The group say they are concerned about the “scientific, medical, epidemiological evidence” and how it has been interpreted by Government ministers.
“For one thing, the process by which the proposed respondents concluded that closing down ‘close contact’ services could (or would) reduce the R number by ‘up to 0.05’ is wholly unclear,” Phoenix Law letter states.
“We will be seeking disclosure of the raw data that was used to come to that figure and an explanation as to how these figures are calculated, to include some indication as to margin of error.”
The group also argues that the Covid-19 policies are not consistent, as churches have remained open, despite being able to offer services online.
The letter also claims there is a degree of political “horse-trading” within the Executive regarding restrictions across Northern Ireland.
“This is wholly inappropriate, and it stands to reason that the measures-imposed ought to be justified only by reference to the expert scientific/medical evidence, properly interpreted,” the letter adds.
“This concern flows from comments made by the Environment Minister (Mr Poots MLA) on the BBC Talkback programme aired on 16 October 2020.
“The applicants believe that Mr Poots stated that – in respect of school closures – the DUP did not wish to see schools closed whereas other members of the Executive wished to see them closed for four/six weeks and so a compromise was reached at two weeks.
“This statement from Mr Poots, at the very least, strongly implies that specific restrictions have been composed by the Executive, not by reference to hard data and scientific/medical evidence and advice, but rather on the basis of a political negotiation between ministers from different parties within the Executive.”
The group also say that the decision to close all barber shops and hairdressing salons has brought considerable personal, business and financial difficulties.
The also said that it has brought “distress and has profound consequences” for the viability of the industry.