Calls in Parliament for a dedicated visa route to be provided for au pairs post-Brexit have been rejected by a minister, who said it was “labour on the cheap”.

It was also warned at Westminster taking such action to “deal with a servant problem” would lead to ridicule.

Meanwhile, Brexit critics argued it has taken a shortage of au pairs for some to realise that quitting the EU was “an unmitigated, self-inflicted disaster”.

Pressed on the issue in the House of Lords, Home Office minister Baroness Williams of Trafford said while there was no dedicated immigration route for au pairs, there were other options such as through the Youth Mobility Scheme arrangements, with participating countries and territories.

I welcome the fact we are moving away from the deplorable British habit of paying British workers too little and not training them enough and instead relying on cheap labour from abroad.

Hailing a previous au pair scheme, Tory peer Baroness Hodgson of Abinger said it gave “hard-working families the benefit from flexible childcare and au pairs leaving the UK with improved English and are great ambassadors as well as giving business to our English language schools”.

She added: “Brexit has meant that there is no available visa route to bring au pairs to the UK.”

Lady Hodgson referred to an earlier ministerial assurance that there would be a temporary visa work route for au pairs and urged Lady Williams to “expedite this issue”.

But Lady Williams said there was no plan for such a dedicated provision.

However, she pointed out 20,000 young people had come to Britain through the mobility scheme “to experience life in the UK”.

Tory former cabinet minister Lord Lilley, a prominent Brexiteer, said: “I welcome the fact we are moving away from the deplorable British habit of paying British workers too little and not training them enough and instead relying on cheap labour from abroad.

“I understand the reasons Lady Hodgson gives for wanting an exception in the case of au pairs but I counsel the House that it will open us to ridicule if the only exception we are prepared to make is helping us deal with a servant problem.”

Lady Williams said: “Au pairs certainly are labour on the cheap.”

Labour peer and Brexit critic Lord Foulkes of Cumnock said: “Does the minister agree with me that although we have had critical shortages of HGV drivers, of fruit pickers, of nurses, of doctors and care workers, it takes a a shortage of au pairs for some people to realise that Brexit is an unmitigated, self inflicted disaster?

“When is the Government going to acknowledge this and try and find a new, positive relationship with the European Union?”

Lady Williams said: “He knows very well the problems with HGV drivers and poultry workers are an issue of easing supply chain pressures and they are nothing to do with Brexit.”

Labour frontbencher Baroness Chapman of Darlington said: “This isn’t really about au pairs is it? This is about opportunities for young people.

“Isn’t it correct that the Government didn’t think about opportunities for young people when it did its Brexit deal? Just like it didn’t think about food producers, cultural industries or even the people of Northern Ireland.

She called on Lady Williams to speak to Brexit minister Lord Frost “to make sure that the appropriate changes are made to the Brexit deal that deal with this alongside other problems that they have created”.

But highlighting the youth mobility initiative, Lady Williams said: “I wouldn’t say that was a scheme that was closing down opportunity to young people.”