The show was about the radical Summerhill School in Leiston in Suffolk,[23] and was subsequently nominated for three children's BAFTA awards.

His first film Bright Star was nominated for an Academy Award in the United States for Best Achievement in Costume Design.

In 2012, he appeared in the theatre production of Mercury Fur, taking the part of Naz at The Old Red Lion, Islington.

Also in 2013, Google Analytics released an internal corporate video which featured Alexander as a demanding shopper under the sub-heading "That is what happens when you save on usability".

[29] Alexander also appeared in The Riot Club, the film adaptation of Laura Wade's stage play Posh alongside British actors Sam Claflin, Max Irons and Douglas Booth.

[30] In the independent film Funny Bunny, which first premiered at SXSW 2015, Alexander played Titty, a troubled teenager.

[33] In January 2021, Alexander appeared in a leading role in the Channel 4 and HBO Max drama It's a Sin, which depicted gay life in the 1980s and early 1990s, and the onset of HIV/AIDS.

[39] Their debut single "I Wish I Knew" was released in July 2012 on the Good Bait label, with the band performing as a five-piece group.

The music video featured an appearance from Alexander's Peter and Alice co-star, Ben Whishaw,[45] and former Misfits actor Nathan Stewart-Jarrett.

[47] In the same month, the band's sixth single, "King", was previewed on BBC Radio 1 and selected as Zane Lowe's Hottest Record in the World.

[49] Internationally, the single peaked within the Top 10 of the charts in Australia, Austria, Bulgaria, Denmark, Germany, Luxembourg, the Netherlands, Ireland and Switzerland.

[54] Alexander collaborated with the Pet Shop Boys on their 2019 single "Dreamland"[55] and later released a cover of "It's a Sin" to coincide with his starring role in the drama series of the same title.

On 16 December 2023, during the final of the twenty-first series of Strictly Come Dancing, it was announced that Alexander would be representing the United Kingdom in the Eurovision Song Contest 2024.

[63] Through various interviews and charity campaigns, Alexander has promoted safer sex and HIV screening,[64] and supported initiatives against LGBT bullying.

In 2018, Alexander was part of Sport Relief's attempt to raise awareness of mental health alongside other celebrities Nadiya Hussain and Stephen Fry.

[78] "It is kind of sad to me that we don't have gay popstars singing about men using a male pronoun," he told Digital Spy, "but that could change hopefully.

[80] The award was presented to him by Héloïse Letissier, and in his acceptance speech, Alexander advocated for the LGBT community and Mental Health Awareness Month, particularly in regard to men.

"[82] In October 2018, British GQ posted an interview[83] between Alexander and Alastair Campbell in which he spoke about his struggles with self-harm and eating disorders, his experiences in 2018 with homophobia, and his political views on Brexit and Donald Trump.

In the interview he said he voted Remain in the 2016 referendum, supported Corbyn as Prime Minister and called Trump "repugnant" and "repulsive".

[85] In protest at the ongoing Israel–Hamas war, Alexander signed a letter by LGBT association Voices4London, which accused Israel of committing apartheid and genocide against the Palestinians.

[89] In June 2020, in honour of the 50th anniversary of the first LGBT pride parade, Queerty named him among the 50 heroes "leading the nation toward equality, acceptance, and dignity for all people".

[95] That year, he also broke the Guinness World Record for most objects caught while spinning on a chair in one minute with a total of 27, which was inspired by his Eurovision entry "Dizzy".