He rejected a career in the legal profession and, in August 1980, took up broadcasting on London's Capital Radio, presenting their Chart Show.
Allinson joined BBC Radio 2 in 1997, presenting the Monday–Thursday late night show from 10:30 pm to midnight, which included a mix of music and guests.
Allinson stepped down from the late night slot in June 2004, so he could concentrate on fronting Radio 2's 'Live & Exclusive' series and 'Sold on Song' projects.
With record producer Steve Levine he formed Magnum Opus Broadcasting to "create programming and content we wanted to hear – but could not find – on the radio.
It was also during this period that he became the main stand-in for many weekday presenters when taking their holidays, such as Chris Evans, Simon Mayo, Paul O'Grady, Terry Wogan, Ken Bruce, Sarah Kennedy and Steve Wright.
From 8 January 2006 until 24 February 2007, Allinson presented a regular weekly show on BBC Radio Oxford on Sunday mornings from 9 am to 12 noon.
From 27 October 2014 to 9 April 2021 Allinson presented the weekday drivetime show, before taking on weekend evenings on Magic Radio.
Following on from the departure of Mark Goodier from Greatest Hits Radio, since May 2024, Allinson can be heard hosting the Saturday and Sunday mid morning slot from 9am-1pm.
In addition to this, on 16th September 2024, Since the Greatest Hits Radio 60s launch, Allinson can also be heard presenting the 6 - 10am breakfast show every Monday to Friday.