Burgon was appointed as Shadow Economic Secretary to the Treasury (City Minister) in September 2015 by new Labour leader Jeremy Corbyn.

Burgon was promoted to Shadow Justice Secretary in June 2016 following the organised mass resignations in protest against the leadership of Corbyn.

[8] Burgon attended the 15 February 2003 anti-war protests against George W. Bush and Tony Blair's planned invasion of Iraq.

"[12] In 2004, Burgon first contested a public election as one of the Labour Party candidates for the Wetherby ward of Leeds City Council.

[13] On previous boundaries, the ward's majorities suggested a safe seat for the Conservative Party, and Burgon was unsuccessful in being elected.

[14] Burgon stood for selection as the Labour prospective parliamentary candidate for the 2011 Barnsley Central by-election, coming second to Dan Jarvis after tying in the penultimate round of voting.

[16][17] Prior to the 2015 general election, Burgon defeated local councillor Judith Cummins to be successfully selected by the Leeds East Constituency Labour Party to replace George Mudie.

[27] In an October 2015 Channel 4 News interview, Burgon admitted that, despite having been Shadow Economic Secretary[28] to the Treasury for over a month, he was still yet to meet anyone from the city of London's finance and banking industry, nor could he predict the UK budget deficit for 2015.

[36] He stood in the 2020 Labour Party deputy leadership election, coming third behind Angela Rayner and Rosena Allin-Khan and receiving 21.3% of the vote in the final round.

"[54] He has warned against the consequences of diplomatic tensions between the US and Iran, commenting that Britain could be "dragged into a conflict" and stating that "we don't want to end up being the messengers of Donald Trump".

[55] Burgon has criticised alleged human rights abuses by the Israeli Government in Palestine, and visited the West Bank in March 2016 as part of a group of Labour MPs.

[56] On the BBC's Daily Politics in March 2018, he was asked by presenter Andrew Neil about claims that he had said at a 2016 Labour Party meeting that "Zionism is the enemy of peace".

[58][59] Burgon has previously expressed support for the PSUV government in Venezuela and tweeted a congratulatory message to Nicolás Maduro when he became president in 2013.

On an episode of Question Time in February 2019, Burgon refused to express regret for supporting Maduro following the outbreak of the 2019 Venezuelan presidential crisis.

[60] He has also expressed support for the Communist Party government in Cuba and spoke at a memorial event for Cuban President Fidel Castro following his death in 2016.

It is a failure driven by capitalism's endless focus on profits whatever the cost",[62] and has expressed support for the School Strike for Climate.

[64] In 2021, Burgon put forward a Ten Minute Rule Bill that would ban arms trade with Israel supported by Caroline Lucas, Liz Saville Roberts and Tommy Sheppard.

[65] Burgon was criticised in December 2021 when he appeared on LBC for refusing to condemn the persecution of Uyghurs in China by the Chinese government, having stated that doing so would “fuel anti-Chinese racism in our society”.

[66] On 24 February 2022, following the 2022 Russian invasion of Ukraine, Burgon was one of 11 Labour MPs threatened with losing the party whip after they signed a statement by the Stop the War Coalition which questioned the legitimacy of NATO and accused the military alliance of "eastward expansion".

[68][69] On 6 February 2019, Burgon won a libel case against The Sun newspaper after it falsely claimed that he had performed with a music group who "delighted" in Nazi imagery.