The poll of over 2,000 adults revealed such an extension was supported by all age groups, social grades and UK regions, and also had relatively high support among Conservative and Brexit Party voters.
The call for an extension to the transition period has been echoed by numerous bodies and pressure groups, including the Scottish and Welsh governments.
Two-thirds of respondents (64 per cent) said they agreed with the statement: “The government should request an extension to the transition period in order to focus properly on the coronavirus.” However, just a third (36 per cent) agreed with the statement: “The Brexit transition period must end on 31 December whether a deal has been fixed or not.”
Best for Britain said the responses broke down into predictable support from those who voted for Labour (84 per cent) and the Lib Dems (83 per cent) at the last election, but that the first statement was also supported by nearly half of those who voted Conservative (44 per cent) and a fifth of Brexit Party voters (19 per cent).
An extension was supported by more than 50 per cent of people across all age groups, with 18-24 year olds the most supportive (78 per cent) and 65-plus year olds the least supportive (although still 52 per cent) – meaning there is no generational divide in the country over an extension request.
The SNP has also urged the UK government to “hit pause” on the Brexit negotiations and seek an extension to the transition period while authorities grapple with the coronavirus pandemic.
The party’s Brexit spokeswoman, MP Philippa Whitford, said it would be irresponsible and “an act of economic and social self-harm” to continue “hurtling” towards the transition deadline.
The Focaldata poll also indicated most people would like the government to seek membership of the EU Early Warning and Response System (EWRS) for medical emergencies, after it emerged earlier this month the Department of Health had been unsuccessful in lobbying No 10 to remain a member.
A total of 65 per cent of people in the UK, including 55 per cent of those who voted Conservative at the last election, want the government to seek membership of the EWRS.
The EWRS was set up in 1998 to “allow exchange of information on risk assessment and risk management for more timely, efficient and coordinated public health action”.
The NHS Confederation has identified membership of the EWRS as a priority, arguing that tackling global outbreaks such as coronavirus would become “more difficult if the UK loses access”.
Speaking about the poll, Best for Britain chief executive Naomi Smith said: “It’s simply not reasonable to expect we will have tied up negotiations with the EU by the end of the year while dealing with a warlike emergency. Nor is it desirable.
“By thinking it can complete both challenges at once, the government would be setting itself up for failure with profound economic consequences.
“Most people just want the government to get on with the job at hand so that lives can be saved and normality restored as quickly as possible.”
She added: “The country is simply not in a place to weather two storms at the moment.”
Hope Not Hate chief executive Nick Lowles said: “EU schemes like the Early Warning and Response System and the ventilator procurement programme are critical tools for responding to this urgent public health crisis.
“Healthcare workers are doing a fantastic job, but they cannot fight this disease alone. They need all the help they can get.
“The government must put politics aside and urgently seek participation in these schemes. It would be foolhardy for ideology to get in the way of practical measures to keep people safe.”
The government has recently said it remains “fully committed to the negotiations”, which it said are continuing.
The Independent has contacted Downing Street for comment.
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