Two cabinet ministers were left fighting it out Thursday to join Boris Johnson in the run-off vote to become Britain's next leader, amid fresh warnings of the risk of a "no deal" Brexit.

Foreign Secretary Jeremy Hunt and Environment Secretary Michael Gove are vying to compete against frontrunner Johnson in a ballot of members of the governing Conservative Party next month.

All three contenders have promised to take Britain out of the European Union as quickly as possible, with the current exit date set for October 31.

All have refused to rule out leaving without a deal on future arrangements with Brussels, although Hunt and Gove say they might delay Brexit for a short time if a deal was close.

Meanwhile the Bank of England warned that the risks of a disorderly departure, which threatens huge economic disruption, had increased.

"Domestically, the perceived likelihood of a no-deal Brexit has risen" since May, the central bank said in a statement after announcing that interest rates would remain unchanged.

The race to succeed Prime Minister Theresa May began with 10 candidates, but Conservative MPs have whittled these down in a series of secret ballots.

In the fourth round of voting on Thursday morning, interior minister Sajid Javid was knocked out, while Gove overtook Hunt to hold second place behind Johnson.

Johnson, a former foreign minister and two-time mayor of London, cemented his lead by winning the support of 157 Tory MPs. There are 313 in total, but two ballots were spoiled.

A fifth and final round of voting will take place on Thursday afternoon, after which Johnson and either Hunt or Gove turn their sights on wooing 160,000 Conservative party members.

The winner chosen by those members will be declared in the week beginning July 22, and will then take over from May in Downing Street.

- Warning on no deal -

May announced her resignation as party leader last month after delaying Brexit twice while she tried unsuccessfully to secure parliamentary approval for her divorce deal with Brussels.

The trio hoping to succeed her have been accused of a lack of any real solution to break the deadlock.

The EU has repeatedly refused to renegotiate May's deal, while the British parliament has rejected it three times -- and also voted against a "no deal" Brexit.

Finance minister Philip Hammond said on Thursday that he could not imagine any Conservative government "actively pursuing a no-deal Brexit".

In comments released ahead of a speech later, Hammond warned such a scenario risked Britain's economic prosperity and could trigger an election the Conservatives might lose.

In a hint at a second referendum, he added: "If the new prime minister cannot end the deadlock in parliament, then he will have to explore other democratic mechanisms to break the impasse."

Hunt had come second to Johnson in the first three rounds of voting, but slipped into third place on Thursday, with 59 votes to Gove's 61. Javid won just 34.

Both Gove and Johnson were key campaigners for "Leave" in the 2016 EU referendum, and the former has sought to woo backers by insisting the final two candidates must be Brexiteers.

Gove, whose campaign has been dogged by admissions that he took cocaine two decades ago, said he was "absolutely delighted" at the latest result.

"If I make the final two I look forward to having a civilised debate of ideas about the future of our country," he tweeted.

Johnson, known for his blunders and accused of divisive language, has barely put a foot wrong, though he has made few public appearances.

He said on Thursday: "I am incredibly grateful, but we have much more work to do."

May cast her ballot before heading for her final formal EU summit in Brussels, and will vote later in the day by proxy.

She has repeatedly refused to say who she is backing.

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AFP

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