Mass immigration from the European Union has been used to “destroy” the conditions of British workers, Jeremy Corbyn said today.

The Labour leader was pressed on his party’s attitude to immigration on the Andrew Marr programme. He reiterated his belief that Britain should leave the Single Market, claiming that “the single market is dependent on membership of the EU . . . the two things are inextricably linked.”

Corbyn said that Labour would argue for “tarriff-free trade access” instead. However, other countries which enjoy this kind of deal, such as Norway, do so by accepting the “four freedoms” of the single market, which include freedom of movement for people. Labour MP Chuka Umunna has led a parliamentary attempt to keep Britain in the single market, arguing that 66 per cent of Labour members want to stay. The SNP’s Nicola Sturgeon said that “Labour’s failure to stand up for common sense on single market will make them as culpable as Tories for Brexit disaster”.

Laying out the case for leaving the single market, Corbyn used language we have rarely heard from him - blaming immigration for harming the lives of British workers.

The Labour leader said that after leaving the EU, there would still be European workers in Britain and vice versa. He added: “What there wouldn’t be is the wholesale importation of underpaid workers from central Europe in order to destroy conditions, particularly in the construction industry.”

Corbyn said he would prevent agencies from advertising jobs in central Europe - asking them to “advertise in the locality first”. This idea draws on the “Preston model” adopted by that local authority, of trying to prioritise local suppliers for public sector contracts. The rules of the EU prevent this approach, seeing it as discrimination.

In the future, foreign workers would “come here on the basis of the jobs available and their skill sets to go with it. What we wouldn’t allow is this practice by agencies, who are quite disgraceful they way they do it - recruit a workforce, low paid - and bring them here in order to dismiss an existing workforce in the construction industry, then pay them low wages. It’s appalling. And the only people who benefit are the companies.”

Corbyn also said that a government led by him “would guarantee the right of EU nationals to remain here, including a right of family reunion” and would hope for a reciprocal arrangement from the EU for British citizens abroad.

Labour Leader @jeremycorbyn rules out single market membership after Brexit. “The single market is dependent on membership of the EU” #marr pic.twitter.com/BQ8WEI7hf9 — The Andrew Marr Show (@MarrShow) July 23, 2017

Matt Holehouse, the UK/EU correspondent for MLex, said Corbyn’s phrasing was “Ukippy”.

Corbyn says “wholescale importation” of E European workers are “destroying conditions” and causing redundancies in construction. Bit Ukippy. — Matthew Holehouse (@mattholehouse) July 23, 2017

Asked by Andrew Marr if he had sympathy with Eurosceptics - having voted against previous EU treaties such as Maastricht - Corbyn clarified his stance on the EU. He was against a “deregulated free market across Europe”, he said, but supported the “social” aspects of the EU, such as workers’ rights. However, he did not like its opposition to state subsidy of industry.

On student fees, Corbyn was asked “What did you mean by ’I will deal with it’?”. He said “recognised” that graduates faced a huge burden from paying off their fees but did not make a manifesto commitment to forgive the debt from previous years. However, Labour would abolish student debt from the time it was elected. Had it won the 2017 election, students in the 2017/18 intake would not pay fees (or these would be refunded).

The interview also covered the BBC gender pay gap. Corbyn said that Labour would look at a gender pay audit in every company, and a pay ratio - no one could receive more than 20 times the salary of the lowest paid employee. “The BBC needs to look at itself . . . the pay gap is astronomical,” he added.

He added that he did not think it was “sustainable” for the government to give the DUP £1.5bn and was looking forward to another election.