Labour leadership contender Owen Smith has refused to dismiss the suggestion there are "too many immigrants" in Britain - as he questioned Jeremy Corbyn's patriotism.

Mr Smith, who is running his campaign against current leader Mr Corbyn on a “save Labour” platform, said that in some parts of the country “the way in which we saw rapid influx of – in particular – eastern European migrants after accession of those countries to Europe definitely caused downward pressure on wages”.

Asked whether there are "too many immigrants" in Britain, he responded: "I think it depends where you are".

He added, however, that there were ways to mitigate those impacts, through extra resources for public services, but the Conservative attempt to put a target on net migration was a "bone-headed" approach to policy-making.

"I think in some places the way in which we saw rapid influx of – in particular Eastern European migrants after the accession of those countries to the Europe – definitely caused downward pressure on wages, definitely caused changes to local terms and conditions for some workers in some sectors," he said.

"We’ve got to acknowledge that. There are ways we can mitigate those effects – extra resources…extra money for doctors, schools places."

Mr Smith, who on Monday criticised Theresa May for scrapping the Syrian refugees ministerial post, said: “We should be honouring the great British tradition of being a place of refuge and sanctuary for people fleeing persecution across the world.”

It comes as Mr Corbyn fights a legal battle over his place in the contest, after he was automatically named on the ballot paper without having to secure nominations from the party's MPs. If Michael Foster, a Labour donor who is pursuing the challenge, emerges successful it could mean the whole leadership race is scrapped and restarted.

Appearing on BBC Newsnight Mr Smith also questioned Mr Corbyn’s patriotism, suggesting it is not “part of his make-up”. He added that the embattled leader’s “metropolitan” politics were were at odds with Labour traditions about national identity in England, Scotland and Wales.

Mr Smith, who said he would meet the Nato target of spending 2 per cent of GDP on defence, renew Trident and be prepared to push the button to launch a nuclear strike if he was in Number 10, said: “One of the weaknesses we have had recently is that people worry that Labour isn't serious about security, that it is a lesser issue for Jeremy.

“I'm not sure that's right, but he has certainly got a different perspective on some of those things – on patriotism if you like; and on security, on defence I think I have got a more traditional Labour perspective on that – an old-fashioned Labour perspective, if you like.”

Owen Smith doesn't support privatising the NHS

He added: “I think Jeremy, to be honest, doesn't really understand sometimes the way in which people have a very strong, perhaps socially conservative ... sense of place, sense of where they are from.

“I am not sure I've heard him talking much about Scotland and identity or about Wales and identity or indeed about England and identity…I suspect that Jeremy has got a rather more metropolitan sense of that and that's not one I think is central to the Labour tradition.”

Asked if he was calling Mr Corbyn unpatriotic, Mr Smith said: "I am saying that I think it is something that is not core to his set of beliefs. He has got a set of liberal perspectives and left perspectives on things and nationhood and nationalism and patriotism aren't really part of his make-up."

Mr Smith, who has faced criticism from Mr Corbyn and his allies over his previous work for pharmaceutical giant Pfizer, insisted he was committed to a “100% publicly owned” NHS – which would mean rolling back the involvement of the private sector in areas such as commissioning.

"It allows profit and cost to become the principal driver of services, not clinical decisions or need," he warned.

Owen Smith would press nuclear button

The challenger, who faces a stiff task to overturn Mr Corbyn's support among the party's grassroots activists, warned Labour could be "destroyed" if it did not change course. "We have been the greatest force for social good for 116 years in this country and it would be a tragedy if we were wiped out," he warned.

"And parties can be wiped out - it takes a long time for parties to rise but they can be snuffed out just like that."

Mr Corbyn's leadership received a boost as Sarah Champion – one of the senior MPs who quit their front-bench roles as confidence in his leadership disappeared at Westminster – returned to her shadow ministerial role.The Rotherham MP had said Mr Corbyn's position was "untenable" and the party could be "doomed" as she quit in June

But she has now returned to her post as a shadow home office minister, focusing on women, equality and domestic violence issues, and Mr Corbyn's office urged other rebels to follow her back to the front benches.