The White House and Moscow have reportedly drawn up a 28-point peace plan that crosses many of Ukraine’s stated red lines. Could Kyiv ever accept it?

Also on the programme: the Oxfordshire fly-tipping scandal is raised at Prime Minister's Questions - we ask how big the problem is nationwide; and eighty years on, a verdict on the Nuremberg trials from the son of a Nazi war criminal and the grandson of a British prosecutor.

During a visit to the White House, Donald Trump said Saudi Crown Prince Mohammed bin Salman ‘knew nothing’ about the 2018 murder of Washington Post journalist Jamal Khashoggi. We hear reaction from Khashoggi’s former editor, Marty Baron.

The Home Secretary Shabana Mahmood laid out a string of reforms to the asylum system that would see refugee status become temporary, guaranteed housing support for asylum seekers end and new capped "safe and legal routes" into the UK created. Speaking in the House of Commons, Mahmood told MPs the current system is "out of control and unfair", and said: "If we fail to deal with this crisis, we will draw more people down a path that starts with anger and ends in hatred."

Also on the programme: as Syrians search for those who disappeared during the 13-year civil war, questions remain over missing American Austin Tice.

And an off-duty pilot who tried to cut off the engines of an Alaska Airlines passenger flight with more than 80 people on board, after having taken psychedelic mushrooms, has been sentenced.

In an effort to curb illegal migration, the government is planning the biggest shakeup to asylum rules since World War Two - inspired by Denmark. We examine what lessons the UK can learn from the Danish system - and ask a Labour MP if these sweeping changes will work.

Also on the programme:

A British journalist detained by US immigration officers for more than two weeks has returned to the UK. We speak to him.

And a pub quiz has banned a team for cheating. Are smartphones are spoiling all the fun?

Anonymous briefings that Keir Starmer would fight a leadership challenge have fuelled speculation about discontent with the prime minister among the parliamentary party. We hear that Labour MPs are increasingly openly contemptuous of the PM in their briefings to journalists. 

Also on the programme: the Democrats release emails suggesting Donald Trump was aware of sexual abuse by Jeffrey Epstein; and the knitters of the Shetland Islands tell us they’ve been stitched up by a TV portrayal of their craft.

A London NHS trust has been fined more than £500,000 and a ward manager convicted of health and safety offences over the death of 22-year-old Alice Figueiredo in Goodmayes Hospital. We ask whether the NHS could be doing more to stop preventable deaths in care.

Also on the programme:

And are the BBC's history programmes failing to present a full view of the nation's past? We hear from two historians: Professor Lawrence Goldman, Emeritus Fellow in History at St Peter's College, Oxford and Dr Tessa Dunlop, author of Lest We Forget: War and Peace in 100 British Monuments.

US President Donald Trump has threatened the BBC with a $1bn lawsuit over edits the Panorama programme made to a speech he gave before the January 6 Capitol riots. We assess the significance of the lawsuit and the resignations of the Director General and the CEO of BBC News.

Also on the programme: why Democrats aren’t happy about a deal aimed at ending the longest government shutdown in US history; and on a rare trip back home, a UK-based Russian writer finds out how people are dealing with the war in Ukraine.

The longest shutdown in US history became even more severe today as hundreds of flights were cancelled by the federal government to reduce strain on air traffic controllers, who haven't been paid for five weeks. We hear from travellers, airport staff and a Republican congressman on the growing political pressure to find a deal in Congress that would end the government shutdown.

Also on the programme: one of the pioneers of artificial intelligence tells us why he's profoundly concerned about the potential harm from the technology. And the geneticist who co-discovered DNA, James Watson, has died aged 97. We hear from a lifelong friend.

As world leaders gather in Brazil, Prince William tells them they must urgently work together to prevent further climate change. But how much can be achieved with the leaders of some of the world’s largest CO2 emitters - the US, China, Russia and India - absent from the meeting?

Two prisoners have been wrongly released from the same London prison. We ask a former head of security at HMP Wandsworth how two of its inmates could have been mistakenly freed - and the Labour chair of the Justice Committee about whether the government should take responsibility.

One year after his re-election Donald Trump has wished himself a happy anniversary, but Americans have sent a different message in local and state elections. After big wins for his opponents - how big a setback is it for the US President?

And as the government announces a new national forest - how do you create a good one?