Former Conservative Party leader Iain Duncan Smith said a proposed future skills-based migration system was "moving in the right direction".

The Chingford and Woodford Green MP told BBC Radio 4's Today programme: "By and large it's moving in the right direction, there are question marks about how this will work and what will happen with regards to overall migration, is the Government going to be looking at caps, is it not looking at caps, how will that work?"

Asked if by not controlling immigration it could cost the Conservatives at a general election, he replied: "Yes, I absolutely agree about that and I do think that's why we need to get out there a strong policy that gives an indication of how we would control migration."

Asked if Britain was ready to halt the flow of low-skilled workers to certain sectors of the economy, Mr Duncan Smith, a former work and pensions secretary, said: "British business has got to start thinking carefully about how it employs, how it trains and where it goes on automation."

The UK he argued "has got one of the worst records" in training and up-skilling of its own citizens, adding: "That's down to our addiction, as a European businessman said to me, we think the UK is addicted to cheap labour and we've got to get off that."

He said: "I think we should deal with migration on the basis of what we believe is right for the UK. Negotiations are one thing but I don't think people would be too happy that they voted to see a control of migration only to find some idea that we don't control migration that would break the whole idea of controlling our borders.

"So the Government knows, they must know, they have to control migration... Taxpayers have been subsidising businesses to bring in people from overseas for some time."

Shadow Brexit secretary Sir Keir Starmer said the "principle that you treat people fairly when they get here and don't discriminate in this way is right".

He told BBC Radio 4's Today programme: "As for how people are treated when they come here, I think there is deep resentment of the hostile environment that was applied to some people who come here and not to others and that's deeply felt and has been exposed over the last few months, and anything that ensures there isn't that sort of discrimination wherever people come from is a good thing.

"That having been said, if you want a close economic relationship with the EU, then obviously that will involve a discussion about EU citizens.

"I wait to see what the detail is the Government comes out with, but the principle that you treat people fairly when they get here and don't discriminate in this way is right."

French former director-general of the World Trade Organisation (WTO) Pascal Lamy said the "main drama" was not between Europe and the UK, adding: "The main drama happening for the moment is within (the) UK."

He told BBC Radio 4's Today programme: "The notion that you can divide the internal market and remain sort of within the customs union for goods but not in the internal market for services, it technically doesn't work."

He added: "The whole point of Brexit is re-establishing a border which had been removed, that's the issue and that's something which Europeans have to accept because this is what the Brits have decided. Now the problem where the British cannot agree among themselves is what is the thickness of this border."

He went on: "My guess is that there will be a deal between (the) UK and EU, now whether this deal passes the House of Commons is an open question."

Tory Mark Francois (Rayleigh and Wickford), an officer of the Brexit-supporting European Research Group (ERG) warned against the Prime Minister "trying to take Chequers to the House of Commons and losing".

He told BBC Radio 4's World At One: "We've yet to know what the final deal looks like, but if it is based on Chequers then myself and my colleagues in the ERG cannot vote for Chequers because we believe it doesn't represent Brexit. We would like the Prime Minister to change tack and to move towards a more Canada-style free trade agreement, we think that has many, many advantages for the UK.

"But if push really comes to shove and they try to put Chequers through the House of Commons then I and my colleagues will vote against it. In those circumstances the Prime Minister would then want to renegotiate along the lines of a free trade agreement, but far better that she pivots to that free trade agreement now before trying to take Chequers to the House of Commons and losing."