The Conservative leader lost her parliamentary majority in last week's election and is now desperately seeking the backing of the 10 MPs from Northern Ireland's ultra-conservative Democratic Unionist Party (DUP).
EU leaders have voiced growing impatience to start Brexit negotiations, which have already been delayed by the parliamentary election — and on which the clock is ticking.
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"The talks are continuing but I think the events in London today probably will have some impact on that. I think it's unlikely there will be any announcement today," a DUP spokesperson told AFP.
Media reports suggested an agreement could be delayed into next week, but the spokesman said: "I certainly have heard nothing on this side to indicate that."
At least six people died and dozens were injured when a massive fire tore through a 24-storey London apartment block overnight, a fresh blow to the capital less than two weeks after the London Bridge terror attack.
May's office issued a statement saying she was "deeply saddened by the tragic loss of life" but made no mention of the talks with the DUP.
On a visit to Paris on Tuesday evening where she met with French President Emmanuel Macron, May described the talks with the DUP as "productive".
The talks are being closely watched in European capitals as they could delay the expected start of Brexit negotiations next week, as well as change Britain's entire approach to its EU withdrawal.
May has dismissed calls to resign following the dismal election result after calling a vote three years early in the hope of bolstering her slim majority, only to actually lose seats.
A lacklustre campaign saw her high approval rating slip away, and support for her "hard Brexit" strategy — pulling out of the European single market and customs union — now hangs in the balance.
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