Labour took a four-point lead over the Conservatives ahead of leader Jeremy Corbyn's keynote speech at the party conference in Brighton on Wednesday.
The latest YouGov poll for The Times showed Labour on 43%, up one point on a fortnight ago, and showed the Tories down by two points, on 39%. Support for the Liberal Democrats remained unchanged at 7%.
In his speech, Mr Corbyn called the party a “government-in-waiting” and pledged a “new common sense” model for the UK’s public, designed to overturn the Liberal free market economics of the past three decades.
The Labour leader to declared that Grenfell Tower stands as a symbol of a failed political system, and the devastating fire that caused the death of around 80 people was the product of a “brutal” system of disregard for rampant inequality, the hollowing out of public services, and “disdain for the powerless and the poor”.
Mr Corbyn said the snap election called by Prime Minister Theresa May that caused her to lose the Conservatives’ majority had “put the Tories on notice and Labour on the threshold of power”.
"We have become a government-in-waiting," he said. "And our message to the country could not be clearer: Labour is ready.
"Ready to tackle inequality. Ready to rebuild our NHS. Ready to give opportunity to young people, dignity and security to older people. Ready to invest in our economy and meet the challenges of climate change and automation. Ready to put peace and justice at the heart of foreign policy. And ready to build a new and progressive relationship with Europe. We are ready for government."
The Grenfell fire was not just "the result of bad political decisions" but stood for "a failed and broken system, which Labour must and will replace", Mr Corbyn said.
The Labour leader attacked the Conservatives' "ragtag" approach to Brexit and told ministers: "Pull yourselves together or make way."
He reaffirmed his commitment to a National Education Service and promised bold policies on housing including rent controls and a tax on land that developers are not building on.
Additional reporting by PA
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