Analysis of polling of more than 6,700 people found 60.2% favour a public vote if MPs cannot decide, against 39.8% who oppose it, said the Best for Britain campaign and Hope Not Hate.
For the first time, the polling - carried out in mid-December and early January - found a majority in favour of a second referendum in every part of Great Britain.
The analysis showed support for a second referendum is particularly high among Labour voters, with a majority in every seat held by Jeremy Corbyn’s party.
The findings come as the Labour leader is under pressure to commit his party to a second referendum if he is unable to secure a general election through a no-confidence motion in Mrs May’s Government.
The research is based on “multi-level regression and post-stratification analysis” applied by market research company FocalData to two waves of YouGov polling involving a total of 6,785 voters.
Participants were asked whether, if Parliament cannot decide on the best way forward for Brexit, they would favour a public vote with three options - Remain, Leave with Mrs May’s deal or Leave with no deal.
Excluding “don’t knows”, a total of 60.2% favoured a second referendum, with strongest backing in Scotland (67.7%), London (67.6%), the North West (61.2%), Wales (60.3%), North East (59.8%) and Yorkshire & Humber (58.9%).
Highest levels of opposition were recorded in the South West (44.9%), East of England (44%), East Midlands (43.2%), South East (42.2%) and West Midlands (42.1%)
Support for a public vote was high among Labour supporters across all regions of the country, ranging from 75.1% in the North East to 82.2% in London.
Best for Britain boss Eloise Todd said: “A public vote is the option the people in the country want, and MPs must not ignore that.
“Politicians need to resist the temptation to cobble together a Westminster fudge - it’s those kinds of deals behind closed doors that people rejected in 2016. Instead they should listen to the country, understand that most people now want a say on their future, and let the people decide on Brexit.”
Hope Not Hate chief executive Nick Lowles added: “MPs have had over two years to sort out Brexit and it is becoming abundantly clear that there is not a majority for any one option.
“With Parliament deadlocked, the British public now clearly believe that they should make the final decision through a public vote.
“They overwhelmingly want to take back control and there is nothing more democratic than that.”
Labour MP Virendra Sharma, a supporter of the Best for Britain campaign for a second referendum, said: “Labour voters and members are clear. Brexit is against what we believe, our values and our principles.
“We, as a party cannot fight austerity and deliver better public services while we pay a sky-high Brexit bill. Labour must back a second Brexit vote. It’s the only way out of this impasse. We must let the people decide.”
? FocalData’s analysis is based on YouGov polling of 1,660 people on December 14 and 15 and 5,125 people on January 2-7.