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With less than a week to go before the election, the poll showed the Conservatives' share of the vote had fallen to 45%, down four percentage points since the previous poll published on 18 May.
Labour's share of the vote increased six points to 40%, according to the poll which was published by the London Evening Standard newspaper.
The poll is the latest to show a narrowing lead for Mrs May.
A YouGov opinion poll on Wednesday showed the Conservatives' lead had fallen to a fresh low of three points.
A failure to win the election with a large majority would weaken Mrs May's position just as formal Brexit talks are due to begin, while the loss of her majority in parliament would pitch British politics into turmoil.
Meanwhile, Mrs May has said that a Conservative politician who has been charged with criminal offences related to spending on the 2015 general election will remain a candidate for next week's vote.
Craig Mackinlay, 50, was charged along with two others earlier today over offences related to campaign expenditure during the election, when he beat Brexit campaigner Nigel Farage in a tightly fought contest.
"The Conservative Party continues to believe that these allegations are unfounded, Craig Mackinlay is innocent until proven guilty and he remains our candidate," Mrs May told BBC television.