Labour leader Jeremy Corbyn has told the BBC he stands by his view that immigration to the UK is not too high.
In a speech on Brexit later he is due to say that Labour is not “wedded” to the idea of freedom of movement.
But he told Laura Kuenssberg that he was not proposing new restrictions on the rights of people to move to the UK.
Instead he wanted an end to foreign workers being exploited in the UK under EU employment rules, which, he said, would “probably” cut numbers.
In the interview with the BBC’s political editor Mr Corbyn was pressed to explain his stance on immigration after the UK leaves the EU, after the suggestions ahead of his speech that he was going to back the idea of restrictions on EU nationals’ current rights to live and work in the UK.
The focus, he said, should be on ending the exploitation of low-skilled workers and more local recruitment – which he said would “probably” reduce overall numbers.
But the Conservatives said the opposition was in “chaos” over the issue and not committed to any controls on immigration while UKIP said working families would not be fooled by what they said was a “load of flannel”.
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Earlier, in a wide-ranging interview with BBC Radio 4, he also said he would personally support a cap on earnings as part of his vision of a more egalitarian country. He also expressed support for striking Southern rail workers, claiming the company had let down the travelling public and its franchise should be nationalised.
Labour says the government has failed to make clear what its objectives are ahead of the start of Brexit negotiations in April, but Mr Corbyn has come under pressure himself to spell out his position on the single market and immigration.
In a speech later, the party leader will argue the UK “can be better off” after leaving the EU and will insist that Labour is not “wedded” to the continued free movement of EU citizens in the UK as a “matter of principle”, supporting “fair and reasonably managed migration”.
There has been growing support among senior Labour figures for restrictions on freedom of movement, although EU leaders have said this is incompatible with continued membership of the single market.
Mr Corbyn told Today that any limits on existing freedom of movement rules would form part of the negotiations and hinge on what kind of access that the UK would get to the single market.
Analysis by Iain Watson, BBC political correspondent
He denies it’s a reboot of his leadership – ‘I’m very well shod’ – but Jeremy Corbyn will certainly be changing his tone in the speech he’ll give on Brexit today.
The trouble is, there’s no obvious change in substance. He’ll say, for the first time, that Labour is not “wedded” to the free movement of EU workers but it looks like he is prepared to co-habit if that’s the price to pay for favoured access to the single market.
And his solution for bringing unskilled EU immigration down – preventing unscrupulous employers using cheap migrant labour – is very similar to Ed Miliband’s policy. But he shows little interest in imposing quotas, as some of his MPs are suggesting.
He did burnish his credentials as an anti-establishment voice speaking out for those who feel left behind, by floating the idea of an upper earnings cap – but that might make some in his party worry that a Labour Britain wouldn’t be fully committed to attracting highly skilled migrants either.
Asked whether he agreed that anyone without a job offer should be barred from coming to the UK in future, he said: “We are not saying that anyone could not come here because there would be the right of travel and so on.”
“The right to work here would be something that would have to be negotiated,” he added.
The Labour leader said the “grotesque exploitation” of EU migrants by some British companies had to end, saying it had also caused “awful tensions” in communities because of the under-cutting of wages.
But he declined to say what acceptable levels of immigration should be and said the NHS and other public services would be in an “even worse” state than they are without migrant labour.
While the UK was definitely leaving the EU, he said it could not “avoid” having a close trading relationship with the continent.
“What we don’t want to do is turn Britain into a bargain basement economy on the shores of Europe where we continuously reduce corporation taxation, encourage a low-wage economy,” he said. “Instead what we want is a high-value economy with skilled jobs promoting high-quality exports.”
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In his speech later, Mr Corbyn will promise to “push to maintain full access to the European single market to protect living standards and jobs”.
But he will emphasise that Labour will “press to repatriate powers from Brussels for the British government to develop a genuine industrial strategy essential for the economy of the future”.
On Sunday, the prime minister told Sky News it would not be possible to hold on to “bits” of EU membership after Brexit, leading to widespread reporting that she was moving towards leaving the European single market, with restricting immigration a priority.
A Conservative spokesman said it was clear Mr Corbyn would not impose any controls on immigration.
“First he said Labour wasn’t wedded to freedom of movement, now he says that there are circumstances in which he could keep it,” he said.
Ahead of Mr Corbyn’s speech, Liberal Democrat leader Tim Farron said his Labour counterpart was “still no clearer” on immigration.
He added: “He failed to pull a shift to keep us in the EU before the referendum and now he is helping Theresa May, [International Trade Secretary] Liam Fox and [Foreign Secretary] Boris Johnson yank us out of the single market.”