He is probably best known for his role as Charlie Edwards in the British TV drama Hotel Babylon based on the book of the same name. Beesley left the show during the 3rd series.
He has been romantically linked to singer Mica Paris, Australian actress/model/singer Danni Minogue, and Spice Girl Mel B. He used to date actress Susie Amy. Beesley is a follower of Manchester United. On a similarly trivial note Beesley is also known to wear briefs (underpants) as opposed to boxers and is one of the few big name actors who can be seen in them on British television, demonstrating much courage and his comfort with his own body, he has also done many nude scenes.
Max has a step-brother, actor Jason Milligan, who is the husband of former Coronation Street and Cutting It actress Angela Griffin.
He has starred in numerous roles both in the United Kingdom and the United States since this breakout role. In 2001, Beesley appeared opposite singer Mariah Carey in the film Glitter, a critical and commercial failure for which he was nominated for a Razzie Award for Worst Supporting Actor. In Britain, he is best known as the star of the BBC Three medical drama Bodies, which broadcast from 2004-2007. He also starred in BBC One series Hotel Babylon from 2006 till 2008. He left the show in the episode 'Under Pressure' aired on BBC One on 18 March 2008, 'riding off into the sunset' on a Harley Davidson.
On 28 October, 2006 Beesley appeared as a special guest playing piano for James Brown during his performance at The Roundhouse in London as part of the BBC's Electric Proms festival.
In June 2007, he starred in an ITV four parter called Talk to Me written by Danny Brocklehurst. Beesley also appears opposite Malcolm McDowell in the film Red Roses and Petrol.
Max was most recently seen in a five-part BBC thriller, The Last Enemy, also starring Robert Carlyle.
In September 2007 Max was a guest on ITV's Ant & Dec's Saturday Night Takeaway, where he and Jonathan Wilkes were successful against the duo in the lighthearted competition Beat The Boys, narrated by Stuart Hall.
His next major appearance will be in the remake of the classic 1970's Sci-Fi show Survivors. The show is currently in production.