Dominic Raab has told businesses to “invest in innovation” to find solutions to skills shortages after the government pledged to make it harder for workers to come to the UK from abroad.

The foreign secretary, who is Boris Johnson’s de facto deputy, said the government would “plug gaps in specific areas” but suggested that businesses should find ways to operate with fewer staff.

It came as Jeremy Corbyn appeared to back away from Labour’s policy of maintaining and extending freedom of movement after Brexit.

Mr Johnson has announced plans for a new immigration system after Brexit, including a salary threshold for prospective workers coming to the UK.

Asked whether the policy would undermine efforts to plug skills gaps in the UK, Mr Raab told the BBC’s Andrew Marr Show: “We want to be able to plug gaps in specific areas, whether it’s in the NHS or whether it’s elsewhere, but what you don’t want to do is encourage over-reliance on cheap labour from abroad, which has a depressing effect on wages in this country.

“Actually the way to deal with that, for those sectors that are concerned, is to invest in innovation to drive up the productivity of those sectors, rather than just engage in this rather artificial reliance on cheap labour from abroad. That’s better for this country, for businesses but also workers.”

Mr Raab used the housing industry as an example of where there was room for “innovation” to plug skills shortages.

He said: “The nature of the housing market has changed, with modular methods of construction. There are innovative ways [of building] that don’t rely on the same volume of cheap labour from abroad, which boosts the housing industry and also, for workers in this country, changes the nature of what it’s like to work in the construction industry from working on sites in the cold through thick and thin to working in factories and with greater career progress.”

“That’s the kind of innovative approach which is good for the economy, good for workers and stops some of the uncontrolled costs of immigration.”

Housebuilders have warned repeatedly that a shortage of skilled workers such as bricklayers is having a negative effect on their ability to build new homes.​

Responding to Mr Raab's comments, Steve Turner of the Home Builders Federation said: "The industry is making significant progress in incorporating new technology into housebuilding but clearly there remains a need for labour if we are to continue to deliver the country’s housing needs.

"The industry is recruiting and training tens of thousands of new people but clearly after any Brexit, we need to ensure we maintain access to the skills we require."

He added: "Across the country 20 per cent of the [construction] workforce is from abroad. Clearly that rises in the south east and London where well over half the people on sites are non UK-residents.

"Particularly in London, where the housing crisis is most severe, there is an acute reliance on foreign labour. We’ve said throughout that after any deal we need to have access to that labour."

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As both of the major parties faced questions over their approach to immigration, Mr Corbyn refused to say that Labour would maintain free movement after Brexit, saying only: “There will be a great deal of movement.”

The policy adopted at Labour’s conference in September said a government led by Mr Corbyn would “maintain and extend free movement rights”.

However, as The Independent has revealed, the policy is set to be significantly watered down when the party’s manifesto is released on Thursday.

Mr Corbyn told Marr that he believed the policy of extending free movement approved at the conference applied only to allowing immigrants already in the UK to be reunited with their families.

He said: “I think the movers of the motion had in mind the questions of family reunion of people from both the European Union and other parts of the world as well.

“Because what you have is people that wholly, legitimately, make their homes and their contribution here but have an artificial income level put on them if they’re allowed to bring partners or children into this country.”

However, hinting at a much more liberal approach to immigration than the Tories, he said: “We cannot exist in isolation, therefore there has to be migration into Britain in order to maintain our economy and our services. That will be reflected in the policy which you will see on Thursday.”

Earlier, Jonathan Ashworth, the shadow health secretary, had refused to say whether Labour wanted immigration to go up or down.