Broadcasting House

Matt Chorley asks 'Is the Prime Minister's plan for the country working?' Can Keir Starmer survive? Matt visits a fair in Wokingham to get public opinion. Labour grandee Alan Johnson, former Theresa May advisor Lord Barwell and pollster Scarlett McGuire assess the PM's chances. Also a possible breakthrough between Iran and the US? Former Middle East Minister Alistair Birt reacts. We hear of an investigation into rumours that the CIA poisoned England Goalkeeper Gordon Banks at the 1970 World Cup. On the news review, former Sun Editor turned Radio 4 presenter David Yelland, Space expert Alice Bunn. And a World Cup winner - for England's Rugby Team, Maggie Alphonsi.

The Sunday morning news magazine programme. Presented by Paddy O'Connell

The fallout from the local elections continues. Cabinet ministers are told by an MP to challenge PM, or she'll try and trigger a leadership race: will it work? BBC Political Editor Chris Mason has the latest. Lord Blunkett and James Harding, Chloe Hubbard and Michael Booker editors of the Observer, The Mirror and GB news react. Also on BH: a look at what's next in England, Scotland and Wales for the incoming parties, and BBC Russia Editor Steve Rosenberg sends an audio postcard from a very different World War Two Victory Parade in Moscow's Red Square.

The government will give carriers extra flexibility. We've a briefing and hear from the travel industry. Plus, the glory of the dawn chorus from deep in a wood in Buckinghamshire, and Paddy tours a crumbling parliament. On the papers – comedian Grainne Maguire, Jon Williams from the Rory Peck Trust and Greg Jackson, CEO of Octopus Energy.

A suspect is in custody after shots were fired at the White House correspondents' dinner in Washington DC, President Trump was rushed off stage but is unhurt. We hear from inside the room. And as King Charles prepares for a state visit to the US capital, his close friend Jonathan Dimbleby joins us live.