Bhaskar was born in Ealing, London, and grew up living above a launderette in Hounslow, west London. He earned a degree in marketing from Hatfield Polytechnic before landing a job as a marketing executive at IBM. He soon realised that he preferred comedy to marketing and joined forces with an old college friend, Nitin Sawhney, to start a musical comedy double act called "The Secret Indians (non-Asian)" which they first performed in 1996 at the now-defunct Tom Allen Arts Centre in East London. This performance was featured on a BBC magazine show called Reportage. They performed extensively also at the Watermans Arts Centre with numerous other acts at a regular Asian comedy night called "One Nation Under a Groove...Innit". Their real break came when they were performing a show at the Oval House venue in South London where, after a strong review in Time Out magazine by Journalist and Playwright Bonnie Greer, they were approached by Anil Gupta, the Producer of what was to become the BBC Sketch series Goodness Gracious Me.
Bhaskar, the Kumars and Gareth Gates collectively released the official single for Comic Relief in 2003, which spent three weeks at the top of the UK Singles chart and was the second highest selling single of the year.
In 2005 Bhaskar was made an Officer of the Order of the British Empire (OBE) in the New Year Honours List.
His first book India with Sanjeev Bhaskar based on the documentary series became a Sunday Times bestseller in 2007.
In October 2008 he was featured on BBC Radio 4's Desert Island Discs.
On 23 February 2009 Sanjeev was appointed as the University of Sussex's new Chancellor. He was formally installed at the university's summer graduation ceremony on 22 July 2009.
He also featured in a Channel 4 documentary series called The House That Made Me. This show, produced by Nutopia in 2010, recreated his childhood home and introduced him to the characters of his youth.
On 31 October 2014 Bhaskar hosted Kermode and Mayo's Film Review, standing in for Simon Mayo on the BBC's flagship film show. He also played the lead character in the online animation Rajesh Finesse in 2014.
In April 2015 he was given the Outstanding Achievement in Television award at The Asian Awards.
As part of the BBC’s series of programmes on the 60th anniversary of the independence of India and Pakistan, he filmed a BBC documentary series India with Sanjeev Bhaskar with Director Deep Sehgal which was broadcast to coincide with the 60th anniversary of Indian Independence in August 2007. According to the BBC it included "an emotional journey" to his father’s ancestral home which is now in Pakistan.
