Corbett was born in Guiseley, West Riding of Yorkshire, on 28 March 1948. In the late 1960s he had to choose another name when joining the performing arts trade union Equity, as there was already a Peter Corbett registered. He kept his surname and chose to go by the first name Matthew, retaining the name throughout his television career.[3]
Corbett appeared in the Doctor Who serial The Dæmons (1971) as a character called Jones[4] and was a regular performer in the Thames Television children's show Rainbow, where he sang and performed and wrote with Rod Burton and Jane Tucker as Rod, Matt and Jane, later on known as Rod, Jane and Roger and finally being better known as Rod, Jane and Freddy.
In 1976, Corbett left Rainbow to take over The Sooty Show from his father Harry, who was retiring (he made a special guest appearance on Rainbow with Sooty in the episodes "1000th Birthday Party" and "The VIP"). Corbett retired in 1998 after 22 years, and chose Richard Cadell to replace him.
In 2006, he and his brother, Dave Corbett, wrote the theme tune for CITV’s Horrid Henry
Corbett contracted COVID-19 in 2020. He nearly died after he contracted pneumonia, which led to atrial fibrillation and had to spend 10 days in intensive care.[7]
As of 2020, he stated he and his wife planned to reside in a retirement village in Horsham, West Sussex.[7]