The YouGov survey for The Times, puts his party one point ahead of the Conservatives following George Osborne’s Budget announcement on Wednesday.
Labour is on 34% while the Tories took 33%. Ukip was on 16%, YouGov said, while the Liberal Democrats trailed with 6%.
The same survey found that 51% of respondents felt the Conservatives were handling the economy badly.
The poll's results have been welcomed by Richard Burgon, MP for Leeds East and Shadows Cities Minister, who today explains why the Budget's 'unfairness' may have contributed to the Conservative party's slump in ratings.
Richard Burgon said: " The key words which define George Osborne's Budget Statement are 'failure', 'excuses' and ‘unfairness’.
"Just a few months ago, in his Autumn Statement, George Osborne painted a rosy picture of the economy but this week he admitted “the storm clouds are gathering” as he missed his own targets, with forecasts for growth, productivity, wages and business investment are all down. Under Osborne, debt as a share of GDP has increased to nearly 84%.
"Despite repeat warnings from economists that his austerity programme wouldn’t work and would drag the economy down, he littered his speech on Wednesday with excuses. According to the Conservative Chancellor, his failure is everyone’s fault but his own.
"Osborne ploughed ahead with giving freebies to his friends. The biggest beneficiaries of his income tax changes are not those on middle and low incomes but the most wealthy. And his changes to corporation and capital gains tax benefiting the powerful financial interests that have been allowed to get away with avoiding paying their fair share of taxes for far too long.
"And to make matters worse, he is funding these giveaways on the backs of the most vulnerable in society. There are massive reductions in support for people living with disabilities, with Personal Independence Payment cuts coming on top of cuts to Employment and Support Allowance. The number of households forced into debt is rising, 81% of his cuts hit women, and in reality, Osborne’s austerity cocktail leaves a bleak future for our young people.
"And through all the bluster about the Northern Powerhouse, there was little gain for Leeds or Yorkshire in Osborne’s so-called ‘devolution revolution’. In fact, the Chancellors business rate cut to small businesses - who have struggled to access the finance they need in recent years – hits council finances whose budgets and services have already been slashed.
"Local Education Authorities will lose control of schools as they are all turned into academies, with no choice for parents or staff. And this does nothing to tackle the issues of insufficient school places and staff shortages.
"He gave the green light for a new High Speed rail link between Leeds and Manchester, but so far has only committed £60 million to develop plans - for a project that could cost £5bn, when we know only one in five projects in his infrastructure pipeline is under construction.
"He promised a total of £150 million for new flood defence schemes across the country, but how much of this will come to Leeds is unclear as York, Calder Valley, Carlisle and wider Cumbria – quite rightly – require investment in flood defences too.
"George Osborne has now been Chancellor of the Exchequer for six years and it's about time he took responsibility. Rising inequality and economic failure has happened on his watch, due to his economic approach. Conservative cuts are hurting ordinary people and our public services – but they’re not working, even by the Conservative Government’s own tests.
"We need a real alternative to George Osborne’s record of failure and unfairness. Labour stands for a high-wage, fairer and more prosperous economy of the future. Something which it’s clear cannot be delivered by this failing Chancellor."