Miquita was born in Paddington, London. Her mother is former Rip Rig + Panic singer and television presenter Andrea Oliver, and her father is an art history teacher. Miquita Oliver attended Holland Park School. In 2001, aged 16, she became presenter of the Channel 4 music show Popworld, co-presenting with Simon Amstell. The pair were known for employing a great deal of humour in interviews. They left the show in 2006, but Oliver continued to present the T4 strand. After an incident in mid-2010 in which Oliver was overheard insulting singer Kesha behind her back by Kesha's management, Oliver was suspended from T4 for six weeks and subsequently her contract was not renewed. She recorded her last T4 in December 2010.
She has hosted shows on both BBC Radio 1 and BBC Radio 1Xtra, notably covering for Sara Cox and Spoony. She left her early morning show Oneclick to focus on TV projects. On 13 December 2007, during her appearance on the TV show Never Mind the Buzzcocks (which was hosted at the time by Simon Amstell), Oliver implied that she was sacked from BBC Radio One following a comment she made in an interview with NME magazine, about Fearne Cotton, calling her a "Devil Woman".
Oliver made a brief appearance in May 2007 on the BBC programme Neneh & Andi Dish It Up – which is presented by her mother Andrea and "Auntie" Neneh Cherry – and has also made appearances on political talk show This Week, on 25 June 2009 and 17 December 2009. In March 2010 Oliver made a programme for Channel 4's T4 called "Miquita's Oliver". She was set the challenge of starting a one-off urban production of the classic musical Oliver! from scratch. She had to cast it, script it and then direct it. The finished product was performed at the Hackney Empire to surprising critical acclaim.
She then went on to have her own television show, called The Month With Miquita, which she hosted on the 4Music channel. She continued to present programmes for T4, such as T4 Movie Special in August 2011.
In November 2011, Oliver filed for bankruptcy after non-payment of a tax bill. In December 2013 she presented the programme 'Young, British and Broke: The Truth about Payday Loans' on BBC3. She said that her own experiences of bankruptcy made her passionate about making the show.
Oliver's godmother is Holby City actress Amanda Mealing.
Oliver was a part of the four-part BBC TV series "24 Hours in the Past", along with Colin Jackson, Alistair McGowan, Ann Widdecombe, Tyger Drew-Honey and Zoe Lucker which went out between 28 April and 19 May 2015 on BBC1.
In 2009, Oliver hosted a Miquita Does series:
- "Miquita Does American Boys"
- "Miquita Does All-Time Floorfillers"
- "Miquita Does Number 1s"
- "Miquita Does Movies"
- "Miquita Does Pop"
- "Miquita Does Power Ballads"
- "Miquita Does Urban Anthems"
In 2008 Miquita Oliver along with vinspired.com helped launch Fashion Favours, a collection of reworked fashion items, customised by volunteers from around the UK. On 25 September 2008, to promote fashion favours, Miquita modelled Prime Minister Gordon Brown's shirt.
On 25 June 2009, Oliver appeared on political talk show This Week to discuss issues relating to fashion – namely Speaker John Bercow's decision not to wear the traditional robes, and French President Nicolas Sarkozy's decision to ban the burqa in France.