The poll by the Kantar covered in the Daily Mirror on Wednesday showed that the Labour was up four points compared to a last similar survey conducted in March to attain at 35 percent of public support while the Tories had lost nine points to stand on a measly 32 percent.
The results came after a chaotic month in the British politics where the government of prime minster Theresa May has failed to break a parliamentary deadlock over her European Union withdrawal agreement.
The public in Britain is becoming increasingly frustrated with the way the Conservatives have handled Brexit as many blame internal divisions in the party for the failure to leave the EU on time.
The UK government had been supposed to leave the EU at the end of last month. It is now seeking another extension to membership beyond the new departure deadline of April 12.
The new poll shows Labour leader Jeremy Corbyn has a high chance of leading his party to a victory in the May 2 local elections where some 8,200 seats are up for grab.
Corbyn and the Labour have campaigned for closer post-Brexit ties to the EU while their call for a public vote on any divorce deal that Britain may get has become more popular over the past months.
The Kantar poll showed that more than half of the respondents, around 51 percent, were in favor of a final referendum on government’s Brexit deal. Some 32 percent said they did not want a public vote on the deal and the rest said they did not know.