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Lib Dem MP Tom Brake says he wants the PM to "adopt a more consensual approach to politics", and in particular, soften her stance on Brexit.

In that vein, Deirdre Brock, of the SNP, says her party will "work with anyone who produces progressive policies", but there's "no mandate" for further austerity and the SNP will oppose any moves by Theresa May to continue it.

Immigration will also be "a sticking point", she adds, because Scotland doesn't want to reduce its new arrivals.

Today Programme
BBC Radio 4

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There have been some concerns raised about the DUP's more socially conservative stance on certain issues - opposition to same-sex marriage, for example - and whether Theresa May could be forced to offer concessions in some of those areas.

But Alastair Ross, former DUP minister, brushes aside such matters.

"I don't expect the DUP will raise any social issues in these discussions," he tells the BBC.

"Those are all devolved matters... therefore I don't expect any of those issues to be relevant."

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Alastair Ross, who was a DUP minister at the Northern Ireland Assembly until its recent collapse, says his party will be looking at what it can "extract from the government".

That means greater investment for Northern Ireland, greater powers, for example over the right to set corporation tax levels, and greater safeguards for a friction-free border with the Republic after Brexit.

Mr Ross says the Tories should be worried if they can't reach a comprehensive confidence and supply agreement and instead have to seek support from the DUP on an issue by issue basis as they go along.

"The price could be much higher and you're bringing instability into this Parliament," he adds.

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Cabinet minister Damian Green insists the Conservative Party has not cut the police budget.

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Mark Harper, former chief whip and now backbench Conservative MP, says despite the lack of a Tory majority, the public have spoken and "it's clear they wanted Theresa May to be prime minister rather than Jeremy Corbyn".

He insists the Queen's Speech is "a big, ambitious package but one which we bring forward with a degree of humility" given the general election result.

Away from Westminster, there'll be a European Council meeting in Brussels on Thursday. As you'd expect, the UK will be somewhat on the fringes, but the prime minister will play a role - before moving aside - as the UK-EU correspondent for MLex tells us...

• The Queen's Speech will take place at 11.30 BST, setting out government legislative plans for the next two years
• Brexit is set to dominate, with up to eight bills, plus other measures including strengthening consumer rights and domestic violence protection
• First Secretary of State Damian Green says controversial social care plans set out in the Tory manifesto have not been abandoned and a consultation will be included in the speech
• Other elements are likely to be watered down or removed - with the scrapping of the triple lock on pensions and the means-testing of winter fuel payments among those most likely to go
• There will be less pomp and ceremony than usual due the late notice of the event
• It takes place against the backdrop of continuing talks between the Conservatives and the DUP over a deal to shore up Theresa May's minority government
• Labour says it will put forward alternatives to the government's plans, especially around ending austerity, arguing the Tories have "forfeited the right to govern"

Today Programme
BBC Radio 4

Just a bit more from Damian Green on immigration.

Chancellor Philip Hammond has been saying in recent days that when it comes to Brexit, jobs and the economy come first, and thereby suggesting that cutting immigration will no longer be the top priority.

Is that the view of the whole government?

"We still think we need immigration at sustainable levels. That was clearly one of the messages behind the Brexit vote," says the first secretary of state.

But Mr Green goes on to say there are "clearly ways you can run the immigration system in the interest of business" .

There will be an Immigration Bill in the Queen's Speech, he adds.

Today Programme
BBC Radio 4

The fundamental question here is whether the wounded antelope - as one senior Tory described her - can change.

There's a strange, superficial and temporary calm on the surface of the Tory party today, but absolute turmoil underneath.

Theresa May has to show she can work differently. She'll say today that she's prepared to work with others and there'll be an element of reaching out - but will that actually happening in the coming weeks, or is it just rhetoric?

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"Theresa May has an enormous sense of duty," says Mr Green, "and it is her duty, our duty, to present our legislative programme and then get on with governing."

"She is exactly the right person to lead that government," he adds, and "will continue to do that for as far ahead as I can see".

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"Plans to reform social care have been anything but abandoned," says Damian Green.

There will be a consultation over the next few months as promised in the manifesto, he goes on, which will include a cap on the amount anyone would have to pay.

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Image source, AFP/Getty

Labour says it wants to amend the Queen's Speech to remove "dangerous cuts" coming for public services, including the police.

Asked about this, Damian Green replies: "There are no police cuts. We have protected police budgets."

He continues to insist that is the case, despite it being put to him that many police chiefs and the London mayor have warned about future reductions in resourcing.

Today Programme
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"The DUP are quite rightly very concerned with the overall economic situation in Northern Ireland," says Damian Green, pressed about their demands for money.

He says the talks are "much wider" than just economics, though, and both parties are "interested in the future success of the whole of the United Kingdom".

"We hoped to get a larger majority," says Mr Green of the election, but he adds: "We won the election. It is our duty to present a Queen's speech.

"And this is not a thin Queen's Speech," he adds, saying it contains a lot about "fighting injustice" and investing in the country.

Today Programme
BBC Radio 4

First Secretary of State Damian Green - effectively the prime minister's deputy is now on Today.

There's still every possibility of a deal with the DUP, he says. "We have some differences, but we have a lot in common."

Mr Green says talks are still progressing, "but all talks of this kind take a long time".

Alison Holt
Social affairs correspondent

With growing demand, squeezed budgets, fewer people getting council help, a shortage of care staff and care companies handing back local authority contracts, it is safe to say this complicated system is in crisis.

For many experts, the Conservative manifesto missed the point on care. It gave with one hand - increasing the amount of people's money that was protected - and took with the other, by including the value of a person's home in all calculations.

But it did nothing about what many see as the fundamental unfairness of a system that leaves some, particularly those with dementia, facing huge costs - sometimes running into the hundreds of thousands of pounds before they get help.

Only four days after the manifesto launch was a cap or limit on the highest care costs promised, but by then the opposition description of a "dementia tax" had stuck.

So has the election shifted the debate significantly? Is there now an appetite for finding a way to share the risk of very high dementia care costs in the way we share the risk of cancer or other health costs?

After putting short-term money into social care last winter, the government was planning a green paper on funding this autumn. The other main parties have also talked about working towards a cross-party consensus.

But what if the government puts social care into the "too difficult to deal with right now" tray? Well, that is described by at least one commentator as grim, because these problems won't go away.