But there was not much in it, with 52 per cent of respondents opposing a new EU poll, and 48 per cent in favour.
The calls for a second referendum – which MPs voted to rule out in March – have increased in recent weeks with politicians from opposing parties considering forming an alliance aimed at stopping a no-deal departure.
Labour deputy leader Tom Watson supports a fresh vote, describing it as the only way to break the Brexit deadlock and arguing that his party should be “loud and proud” in its support for remaining in the EU.
He said he was not surprised to see the results of the Star's survey, and claimed that support for a second referendum was growing in the region due to people's concerns over the negative impact of no-deal.
"We now have information we didn't have during the referendum in 2016," the West Bromwich East MP said.
"And sadly we have discovered that the industrial sectors that will lose out most if we crash out without a deal, are automotive and aerospace manufacturing and the chemicals sector.
"I'm desperately worried on the impact this will have on families and businesses in the West Midlands."
The prospects for a second poll seem slim, as it would require new legislation to be brought in as part of a process which could take months to sort out.
South Staffordshire MP Gavin Williamson, the Government’s Education Secretary, said a second referendum would cause serious damage to British politics.
He said: “We made a commitment to the British people when we had a referendum that we would deliver on the result.
“That is precisely what the Government is focused on.
“To have another referendum would absolutely destroy people’s faith and confidence in politics.
“What people expect is delivery, which is why the Government is putting every effort into ensuring Britain exits the EU by October 31.”
A new Survation poll released in the last few days said Remain would win a second referendum by 55-45, with 15 per cent of people believing that Britain will not leave the EU.
Almost half predicted a no-deal Brexit, while a general election poll showed the Conservatives would win with four per cent more of the vote than Labour, who narrowly edged the Lib Dems into third.