However, the prediction website Electoral Calculus has emphasised that the Conservatvies still have a long way to go.
If the poll reflected an election result the Tories would still have their worst ever return of MPs with 147 and Labour would have a majority of 206.
If non-voters are included in the results, less than one in five (18 percent) would vote Conservative, while barely half (53 percent) of those who backed them in 2019 would still vote for them.
Of the 2019 Conservatvie vote 17 percent would not vote again or are uncertain.
But the recent “chipping away” at Labour’s lead is provinding some Tory MPs with optimism.
One minister told Express.co.uk: “Our vote has been soft in our traditional areas because of issues like tax and so forth.
“The council electins showed our vote was holding up well in the Red Wall areas.
“If our traditional voters start to come back then it will change.”
Another Conservative MP noted: “At the moment people are not focussed on the election but when they do they will ask more questions about Starmer and Labour.
“If by the new year we can reduce Labour’s lead to 10 points or less then we have a real chance.
“We saw with Starmer’s illegal immigration policy that voters did not like it and the number of U-turns they are performing is spectacular.”
Others hope that the fear of a “Rejoiner alliance” with the SNP or Lib Dems will scare voters.
Techne UK chief executive Michela Morizzo said: “On the eve of the Conservative Party Conference our regular tracker poll of current Westminster voting intentions continues to see the gap between the main parties narrow.
“It does seem that last week’s announcement around delaying the stopping of selling petrol and diesel cars to 2035 has found some favour with the wider electorate.
“Not least I would say as this policy approach absolutely helps cost of living pressures for struggling families who need to travel. Further to this, the Home Secretary’s speech earlier this week directly addressing the significant problems around illegal immigration might too be finding some traction amongst voters.
“It will be interesting to see if and what the effect of the Party Conference will be.”