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Liam Fox says a no-deal Brexit could be used as a “weapon” for those “seeking to break up the United Kingdom”.
The International Trade Secretary said the next prime minister should tell the EU we want to leave the bloc with a deal for “minimal disruption”.
But he said no-deal must remain on the table, “otherwise we have no real negotiating hand”.
He also confirmed he would be backing Foreign Secretary Jeremy Hunt in the Tory leadership contest.
Brexit supporter Mr Fox called him an “impressive foreign secretary” who had “deal making [as] part of his DNA”.
The legal default is for the UK to leave the EU on 31 October, with or without a deal.
Theresa May negotiated a withdrawal agreement with the EU, but it was voted down by Parliament three times.
Mrs May steps down as Conservative Party leader on Friday – she will remain PM until a successor is named at the end of July.
There are currently 13 Tory MPs competing for the top job.
The high number has drawn criticism from some members of the party, who are calling for the rules of the contest to be changed to whittle down the amount of candidates.
The executive of the party’s backbench 1922 Committee will meet later to decide the rules and timings for the leadership election.
‘Weapon in that battle’
Speaking to BBC Radio 4’s Today programme, Mr Fox said there were two messages that the next leader of his party – and the country – needed to give the EU.
“Number one is that we want a deal, because we think that is the best way to leave the European Union with minimal disruption,” he said.
“But equally, and it has to be delivered with equal volume and equal strength, if we can’t get an agreement, we have to be willing to walk away, otherwise we have no real negotiating hand.”
One of the main concerns raised by critics of a no-deal Brexit is the risk that a hard border might return between Northern Ireland and Ireland.
This would see checks take place on both people and goods, and some fear that would put the peace process at risk.
When asked if he believed a no-deal would lead to a border, Mr Fox warned some could abuse it for their own gains.
He told Today: “The prospect of a no-deal might well be used by those who seek to break up the United Kingdom, to use that as a weapon in that particular battle, both I think in Northern Ireland and potentially in Scotland.”
Who will replace Theresa May?
The winner of the contest to lead the Conservative Party will become the next prime minister.
Brexit: No-deal could be used as ‘weapon for breaking up UK’, says Fox}