Mountainhead to See How They Run: the seven best films to watch on TV this week

Pick of the week

In Jesse Armstrong’s squirmingly funny satire, four tech moguls gather at a retreat called Mountainhead (a wry nod to Ayn Rand’s paean to individualism The Fountainhead). When the launch of a deep-fake tool by Cory Michael Smith’s billionaire Venis plunges the world into financial and social meltdown, he and his alpha male peers – Jeff (Ramy Youssef), Randall (Steve Carell) and their host Souper (Jason Schwartzman) – insouciantly ponder exploiting this “moment of creative destruction” and taking over the world. As in Succession, Armstrong has a keen eye for the supercilious world of the super-rich, where people are expendable and petty grievances can be dressed up as utopianism.
Sunday 1 June, 9pm, Sky Atlantic

See How They Run

Sam Rockwell and Saoirse Ronan in See How They Run. Photograph: Parisa Taghizadeh/Disney

Part affectionate throwback to classic Agatha Christie, part knowing sendup, Tom George’s engaging comic whodunnit is set in the wake of a murder after the 100th West End performance of The Mousetrap in 1953. The corpse is lecherous American director Leo Kopernick (Adrien Brody), who was due to film a version of the play. Sozzled Insp Stoppard (Sam Rockwell) and eager, naive PC Stalker (Saoirse Ronan) are put on the case, with a star-stuffed cast of suspects – Ruth Wilson, David Oyelowo, Reece Shearsmith, Harris Dickinson – joining in the fun.
Saturday 31 May, 9.20pm, Channel 4

Inside Out

Relax … Amy Poehler and Phyllis Smith in Inside Out. Photograph: Moviestore/Rex Shutterstock

Pete Docter’s relentlessly inventive animation spins a touching yarn out of the competing emotions that swirl around a child’s brain. Joy (a chipper Amy Poehler) is the controlling voice in the head of 11-year-old Riley. But when the girl and her parents move to a big city, San Francisco, the other feelings – Anger, Fear, Disgust, but principally Phyllis Smith’s Sadness – come into play. An error in the handling of core emotions sends Joy and Sadness on a desperate quest into the weirder recesses of Riley’s mind to save their charge in a bitter, sweet tearjerker.
Sunday 1 June, 3.30pm, BBC One

The Three Burials of Melquiades Estrada

Tommy Lee Jones and Barry Pepper in The Three Burials of Melquiades Estrada. Photograph: The Kobal Collection

Tommy Lee Jones always appears most at home on screen with a stetson, a horse and a noble purpose. For this rare 2005 foray into directing, he gave himself a plum role as Texas ranch foreman Pete, who is determined to honour the last wishes of his friend and colleague, illegal immigrant Melquiades (Julio Cedillo), shot dead by trigger-happy border patrolman Mike (Barry Pepper). A modern western with a social conscience and a dose of mordant wit, it also has time for those genre staples of self-sufficiency, friendship and loyalty.
Sunday 1 June, 9pm, Great! Action

Blue Road: The Edna O’Brien Story

Blue Road: The Edna O'Brien Story. Photograph: Modern Films/PA

A woman who lived her life battling the repression that is an enduring theme in her novels, Irish author Edna O’Brien is a terrific subject for a documentary. Sinéad O’Shea does her proud here and is blessed with access to the then 93-year-old – who is as sharp as ever when talking through her experiences. But O’Brien is also tinged with melancholy – a result of a traumatic childhood, an oppressive marriage and the misogynist resentment she faced – not least back in Ireland – due to her frank opinions.
Sunday 1 June, 9pm, Great! Action

In the Loop

Peter Capaldi as Malcolm and Tom Hollander as Simon in In the Loop. Photograph: Nicola Dove

Armando Iannucci’s 2009 comedy bridges the gap between The Thick of It and Veep by throwing together governmental fools and chancers from the UK and US. It also ups the ante by making the result of the bungling of its apparatchiks, spin merchants and elected officials an actual war. Most of the Thick of It cast return, though confusingly as different characters. Luckily, Peter Capaldi’s vituperative director of comms Malcolm Tucker is present and incorrect, bullying the out-of-his-depth minister for international development Simon Foster (Tom Hollander) on an ill-fated visit to Washington DC.
Tuesday 3 June, 11.45pm, BBC Two

National Anthem

Charlie Plummer in National Anthem.

New Mexico casual labourer Dylan (Charlie Plummer) is getting by day to day with his alcoholic mother and younger brother, until he gets a casual job at the House of Splendor ranch. It is home to – and refuge for – a community of LGBTQ+ folk, in particular rodeo rider Sky (Eve Lindley). Her and Dylan’s mutual attraction is instant, though she is already in a relationship that maybe isn’t as open as she says and he hopes. Luke Gilford’s queer coming-of-age drama is a warm-hearted tale of finding your people, set in a bigotry-free environment that keeps the political personal.
Wednesday 4 June, 11.20pm, Film4