We're ending our live coverage in the Politics Hub for today.

Be sure to join us again tomorrow for the latest updates in politics as they happen.

Sophy Ridge now turns to the thorny issue of the two-child benefit cap which the prime minister is facing pressure to drop from some of his own MPs.

Baroness Smith points to the fact that Sir Keir Starmer has already set up a child poverty taskforce as evidence the party wants to tackle the issue.

But asked about the cap, she says her government "can't make any promises" and that scrapping the cap would cost £3bn.

"We have very clearly said that we're not going to make promises or do things that are going to plunge the economy back into the sort of mess that we've inherited, that we're now having to clear up," she says.

"But child poverty is at the heart of a Labour government, and that's why in a whole range of ways reforming housing, bringing in breakfast clubs."

Ridge interjects to raise objections to the cap from Labour MPs, including Rosie Duffield, who branded it a form of "social cleansing".

Sophy Ridge is now talking to Baroness Smith, the former Labour home secretary who was appointed minister for higher education in Sir Keir Starmer's cabinet.

She is asked about the funding crisis facing universities, in part caused by a drop in student applications and the restrictions on international students bringing family to the UK.

She says universities should be "looking at how they can run efficiently as possible".

Asked whether there was the possibility that some universities may have to close, Baroness Smith replies: "I don't want that to happen. And I'm concerned that students are still able to get those opportunities."

Pressed again on whether some higher institutions could close their doors, the minister again says: "I hope it doesn't happen.

"And, you know, that's what we need to work to try to avoid."

You can read more from Sky News below:

Back to UK politics, our deputy political editor Sam Coates tells Sophy Ridge that tackling illegal and legal migration is dominating the agenda.

He says Sir Keir Starmer is "very deliberately not abandoning" some of the measures that were announced by the Tories on migration, including restrictions on overseas students bringing family members.

He says it remains to be seen whether the prime minister's own plans to curb migration, including its new Border Force Command, will make a "big difference" or not.

"It may be that just this plan of attacking the opposition - now the Tory party - is the best thing that will get through to the public," he says.

Back in the UK, Sophy Ridge welcomes former Labour MP Jonathan Ashworth and Reform deputy leader Richard Tice to the studio.

They both agree that Mr Biden's withdrawal from the race was "inevitable".

Mr Ashworth, who lost his Leicester seat in the election, says the outcome means the race has "upended" and is more "open".

"If you had asked me a week ago when Biden was still in the race, I would have said Trump has got it," Mr Ashworth says. 

"I think it's slightly more open now.

"As Keir Starmer said today, he is a prime minister leading a government and he will obviously want to work with whoever is elected US president because our relationship with the United States is so important."

Mr Tice says Trump was "heading towards victory regardless" but questions whether Ms Harris could defeat the Republican nominee.

"There is a reason why she hasn't been used when Biden has been struggling in a significant way," he says.

Sky News correspondent David Blevins tells Sophy Ridge that Kamala Harris looks all but set to replace Joe Biden as the Democrats' presidential candidate after the president pulled out the race.

Speaking from Washington, he says: "I think we are looking at a coronation that will be described as a contest."

He notes she has received a number of high-profile endorsements, including from Mr Biden, former president Bill Clinton and former speaker Nancy Pelosi.

Blevins says that at an event today, she did not formally launch her campaign but "did take the opportunity" to pay tribute to Mr Biden.

Our weeknight politics show Politics Hub With Sophy Ridge is live now on Sky News.

The fast-paced programme dissects the inner workings of Westminster, with interviews, insights, and analysis - bringing you, the audience, into the corridors of power.

Sophy speaks to new higher education minister and former home secretary Jacqui Smith about the challenges facing the sector.

On Sophy's panel are:

• Jonathan Ashworth, chief executive of Labour Together, former Labour MP for Leicester South and shadow paymaster general;
• Richard Tice, deputy leader of Reform and MP for Boston and Skegness.

Watch live on Sky News, in the stream at the top of this page, and follow live updates here in the Politics Hub.

Watch Politics Hub With Sophy Ridge from Monday to Thursday on Sky channel 501, Virgin channel 602, Freeview channel 233, on the Sky News website and app or on YouTube.

By Tamara Cohen, political correspondent

Now installed in the Home Office, and the new government having scrapped the Rwanda scheme, Cooper revealed it had cost taxpayers £700m.

That's £290m for the payments to Rwanda, plus the chartered flights, the airfields, the hundreds of civil servants working on it and unable to send anyone there, except four people who had volunteered go.

Without intervening, she said, it would have cost £10bn over the six-year period of the partnership. Labour's measures would, she said, save £7bn. 

This hits the two key points of Labour's narrative - that the Conservatives crashed the asylum system (or the health service, prisons, the economy...), and that Labour's medicine will involve better stewardship of the public finances. 

Tucked away at the end of her statement is that Labour will end the retrospective application of the Illegal Migration Act - passed in March 2023 and meaning all migrants arriving since that date are awaiting detention and cannot be processed - and either allowed to stay or returned. This is key to the party tackling the ballooning backlog of cases. 

Her opponent James Cleverly called it "an effective amnesty for thousands of asylum seekers", and questioned where those allowed to stay would be housed. 

In the questions afterwards, it was notable how many Labour MPs asked questions about how the government would gain control over migration, and said their constituents were concerned about it.

Cooper warned that high levels of small boat crossings would persist over the summer. The government has already advertised for a Border Security Commander and has announced £84m to keep migrants in their home countries. By next summer, MPs will want to see not just savings - but evidence of results. 

You can read more from Sky News below:

Away from the Commons, defence Secretary John Healey is speaking at the RUSI Land Warfare conference.

He says the Labour government will have an "unshakeable commitment to NATO" and a "total commitment to spending 2.5% of GDP on defence".

But the government has so far refused to put a date on when that figure will be reached.

Healey also said he wanted a "national, unified response" to military threats, including the war in Ukraine.

"I’ve already offered the shadow defence secretary access to intelligence briefings," he revealed.

Yvette Cooper, the home secretary, has been giving a statement to the Commons on border security.

Speaking to MPs, she said the previous last government planned to spend "over £10bn" on its Rwanda deportation scheme.

Cooper also said £700m had already been spent on the policy "in order to send just four volunteers".

She branded it the "most shocking waste of taxpayer money I have ever seen".

But James Cleverly, the shadow home secretary, accused Cooper of using “made up numbers”.

Cleverly, who was home secretary before the election, criticised the new Labour government for having scrapped the Rwanda policy on purely "ideological grounds".