The family of the broadcaster said on Tuesday (29 August) that Crick died following a “short illness”.
A spokesperson for Bauer Media UK said: “Jamie Crick was a broadcaster through and through and played an integral role on our radio stations.
“He was also a great friend to his colleagues at Jazz FM, Scala Radio and the wider Bauer Media teams. He will be sorely missed by them all, along with his friends and listeners.
“Our radio stations have a big gap to fill and will pay tribute accordingly in the near future, but while they all come to terms with Jamie’s unexpected passing, they will continue to broadcast the music that he loved in his honour every day.
“Our deepest condolences are with his family and loved ones at this time.”
Crick presented his final Jazz FM show on Monday (28 August). On the programme, he played tracks ranging from Roy Ayers’s “Everybody Loves the Sunshine” to The Dave Brubeck Quartet’s “Take Five”.
He signed off from his show with the words: “I will see you in couple of weeks, I’m just going to go and enjoy the rain.”
The presenter joined Jazz FM in 2014 as a guest presenter before taking over the breakfast show and then moving to the afternoon slot in 2016.
He had spent around 20 years on Global’s Classic FM from 1994 onwards, and was creative director of the UK’s first LGBT+ station Gaydar Radio, which he helped launch.
Fellow radio presenter Simon Bates wrote on X, formerly Twitter: “So very sad to learn that Jamie Crick has died. When I first started at Classic FM, Jamie was a fund of support, kindness and good humour.”
BBC South and BBC South East deputy managing editor Mark Carter, who saw Crick join the corporation’s local teams, wrote: “Hugely saddened to hear of the passing of Jamie Crick. Long before his national career, I heard Jamie on County Sound and thought… that’s the kind of presenter I’d like to be.
“Many years later, I was only too pleased to welcome him into the @BBCSussex @BBCSurrey family.”
Crick also co-founded Encore Radio, which celebrated the music of musicals, in 2018 and also presented a programme about the form of theatre on Bauer’s Scala Radio.
Nick Pitts, content director of Jazz FM, also paid tribute to the late broadcaster, writing: “I am very lucky. I get to make friends with some amazing people who I also work with. @Jamie_Crick was one of those very special people who I had a lot of time for.
“Someone who cared for others, loved being on the air and today, someone who has left our world.”
Additional reporting by Press Association