Sir Mike Penning has claimed that Europe needs to change its stance on the UK leaving the EU or it will "be much more difficult for them than it is for us".
In an interview with Julia Hartley-Brewer, the Conservative politician said that "Europe needs to come up with a much better offer" for the UK.
"She [Theresa May] needed to know, and the rest of Europe needed to know, that loyalists here won't support it [Chequers], in which case it is dead as a dodo. And Europe needs to come up with a much better offer to us otherwise it will be, not just a little difficult for them, I think it will be much more difficult for them than it is for us.
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"I'm loyal to the referendum, I'm loyal to my constituents, I'm loyal to my party. If she tries to force Brexit as it is through the house of commons, we'll vote it down, because it doesn't deliver what the people ask for.
"If she's being advised that she could push a version of Chequers through the house of commons and put people like me on the naughty step, she's very, very wrong."
Hartley-Brewer asked if it was "possible for May to dump the Chequers deal", or if it would result in her resignation as Prime Minister.
"There's no way that there should be, can be and would be a leadership election while the negotiations are going on. That would be very silly," Sir Mike replied.