Recorded on a weekly basis, the show takes a look at issues relating to Brexit, the term for the United Kingdom's withdrawal from the European Union, explaining the subject to listeners in an informative but light-hearted fashion.

[3] Prior to Brexitcast, a similar podcast titled Electioncast was launched in 2017 to cover that year's general election.

[8] On 5 December 2018 the Brexitcast team of presenters appeared on BBC One's The One Show to answer Brexit-related questions from the audience ahead of a planned vote in the House of Commons.

[11][10] It was also confirmed that Brexitcast would continue to be available as a downloadable podcast, with extra editions recorded to coincide with significant events.

[13] On 10 October, the journalist and musician Rhodri Marsden appeared as a guest on the programme where he debuted tracks from his Brexit-inspired disco concept album The Hustle.

[4] In November 2019, a discussion on Brexitcast about "shitposting" attracted some media comment after Kuenssberg gave an incorrect description of the term.

[15][16] The edition aired on 30 January, the day before the UK's exit, was recorded before a live audience at London's BBC Radio Theatre.

[18] The first edition of Newscast aired on 6 February, and while continuing to discuss Brexit, also focused on other events such as the 2020 Irish general election.

[23] Charlotte Runcie, writing in The Daily Telegraph, described Brexitcast as "excellent...funny, well-informed and refreshingly sane", but questioned whether the format would transfer successfully to television.

Following the broadcast of the first television edition of Brexitcast, Alison Rowat of the Glasgow Herald questioned the logic of creating a TV version, which she described as "watching four people sitting in a row.

[26] Joel Golby of The Guardian has emphasized the show's nerdish nature, describing Brexitcast as "TV for people who can recite their credit score from memory", and he was largely positive in his review of its content: "While it isn't pretty, it is clever: an informed conversation about the day's politics by people who do that smart-person snicker instead of an actual real laugh".