David Cameron has insisted that the UK Government's plans to cut tax credits for poorer families are "fair" after Boris Johnson became the latest senior Conservative to warn about their impact on the lowest paid.

The London Mayor is expected to tell the Conservative Party conference in Manchester that when the welfare cuts come into effect in April, the Government must ensure it protects people like shop workers and cleaners on whom the capital's economy depends.

The Prime Minister is coming under pressure to rethink the plans, amid predictions that millions of working households will be left out of pocket as tax credits are slashed ahead of planned rises in the minimum wage and further cuts to the personal allowance.

An estimated 60,000 marched in protest against austerity on Sunday, and there was an outraged reaction to suggestions from Health Secretary Jeremy Hunt that cuts in in-work benefits would send a "cultural signal" to Britons to work like the Americans or Chinese.

But Mr Cameron insisted that eight out of 10 families will be better off overall as a result of the Government's welfare and tax changes. Even those who lost out in cash terms would gain from measures like extended free childcare and reductions in social rents, he said.

The Prime Minister told BBC1's Breakfast: "The combination of tax reduction, a higher national living wage and these tax changes, I believe, is fair. They are part of moving the country form a low-pay, high-tax, high-welfare country towards a higher-pay, lower-tax, lower-welfare country."

Mr Cameron also backed Home Secretary Theresa May's warning that mass migration will make it "impossible to build a cohesive society".

Mrs May is expected to use her keynote speech to the conference to warn that millions of people from poorer nations have a "perfectly understandable" desire to live in Britain but there is a limit to the amount of migrants the country can take.

"While we must fulfil our moral duty to help people in desperate need, we must also have an immigration system that allows us to control who comes to our country," the Home Secretary will say.

"Because, when immigration is too high, when the pace of change is too fast, it's impossible to build a cohesive society. It's difficult for schools and hospitals and core infrastructure like housing and transport to cope. And we know that for people in low-paid jobs, wages are forced down even further while some people are forced out of work altogether."

Mr Cameron rejected suggestions that Mrs May - whom he hailed as an "excellent" Home Secretary - was seeking to say that unemployment was the fault of foreigners He told the BBC: "No, what we are saying is that in an open, modern democracy like Britain, yes, we need migration, we benefit from migration, but that migration must be controlled.

"One of the problems we have had in recent years is, because we have created more jobs than the rest of the EU put together, we have seen very high rates of migration."

Mr Cameron said the Government needed to address a situation where new migrants could claim as much as £10,000 a year in in-work benefits as soon as they arrive in the country.

"It's quite clear that we need to do more to bring migration into better balance because, as Theresa will say in her speech, if you want an integrated, successful society, yes, you want immigration, but you want it at a rate where you can properly integrate people and bring them into your society and make sure that the school places are there and the hospitals aren't overcrowded and the pressure on our country isn't too great."

Mrs May has also announced that the Government will stop European Union nationals from making asylum claims in Britain.

Meanwhile, there were calls for Mr Hunt to apologise after he told a meeting on the fringe of the Manchester conference: "There's a pretty difficult question we have to answer, which is, essentially, are we going to be a country which is prepared to work hard in the way that Asian economies are prepared to work hard, in the way that Americans are prepared to work hard? And that is about creating a culture where work is at the heart of our success."

Single-parent charity Gingerbread accused him of "demonising" low-income families, while Unite union general secretary Len McCluskey described the comments as "a disgraceful insult" from the "richest member of the Cabinet".

But Mr Cameron told LBC radio: "You read the top line and I thought 'Oh, hang on, what's going on here?' I then actually read what he said in full and I could see what he was trying to say - and Jeremy has come out very clearly and clarified that - which is that we want Britain to be one of the success stories in the world.

"British people do work incredibly hard. In fact, we've got a greater percentage of our country in work - both men and women - than at any time in our history. So I think, when you look at everything he said, it wasn't quite what people are saying."

In his final speech to the conference as London Mayor, Mr Johnson is expected to tell activists they must use the election of Jeremy Corbyn as Labour leader to truly seize the mantle of the party which helps all people succeed.

Conversations in the conference corridors have been dominated by discussion of who will succeed Mr Cameron as Tory leader, with Mr Johnson widely perceived as falling behind other rivals at the same time as Chancellor George Osborne cements his status as the firm favourite.

Speaking at the conference, Mr Johnson is set to join Tory calls for a fresh look at tax credit changes. He will say: "We must ensure that, as we reform welfare and we cut taxes, that we protect the hardest working and lowest paid.

"Shops workers, cleaners, the people who get up in the small hours or work through the night because they have dreams for what their families can achieve - the people without whom the London economy would simply collapse.

"(These are) the people Labour is leaving behind and then there is an even more important requirement. If people are to feel bound into this system then there must be hope and aspiration, and above all there must be opportunity and it is here that we Tories have a massive advantage.

"Because if Labour is once again becoming the party that pointlessly bashes the rich, it is we who give everyone the tools to make their own lives and their own successes."

Mr Johnson will appear alongside Zac Goldsmith, the Conservative candidate to replace him in City Hall at May's mayoral elections.

Mr Johnson's planned remarks on welfare reform will follow a growing row both inside and outside Tory ranks on tax credit cuts, which have already cleared the Commons.

Mr Osborne has rebuffed critics of cuts to tax credits, insisting it was failure to control public spending that would be "economic cruelty" for working families.

He hit back after David Davis joined Tory demands for a rethink, warning that the squeeze could prove as damaging to the party as the poll tax was under Margaret Thatcher.

The independent Institute for Fiscal Studies has warned that 13 million families will lose an average of £240 a year when the cuts come into effect in April, while three million will lose £1,000 or more.

Mr Cameron said he had no objection to Mr Corbyn's attendance at a rally on the fringes of the conference on Monday, a break with the convention that rival leaders stay away.

But he said the Labour leader's message had been "not very edifying".

"It is a free country; he can go where he likes and say what he likes and I'm not going to restrict his movements," he told Sky News.

"What is more worrying is what he is saying which is that he wants to put up taxes, which would wreck economic security, he wants to give up nuclear weapons, which would wreck our national security.

"So it is not a very edifying message.

"Back here at the Conservative conference we are delivering the security, stability and opportunity that our country needs," he added.