Gordon Brown told the Radio Times that he is backing the campaign to protect the digital station, facing closure as part of a shake-up of the corporation intended to divert £600m into programme-making.
"[I] think, personally, that the BBC should not have succumbed to pressure to cut certain things – but they have," he told the magazine. Asked whether he was in favour of the campaign to save 6 Music, he said: "Yes because it's the next stage you worry about. The Conservatives have said that they'll hive off Radio 1.
"A lot of things that the BBC does are incredibly creative and quite risky. But this is a necessary means of us being a creative society."
The prime minister added : "I want to safeguard the independence of the BBC and I think the licence fee is the means by which you do it."
He described the licence fee as "essential" to the BBC, adding: "Any proposal to massively cut the fee or to strip the BBC of its independence – or alternatively, to remove its ability to make certain programmes – is a huge mistake.
"I don't think politicians should make that decision about what the BBC produces. I think the BBC should make that decision."
Asked whether he preferred listening to Chris Moyles on Radio 1, Chris Evans and Jeremy Vine on Radio 2 or Jarvis Cocker on 6 Music, he replied: "Definitely 6 Music. Definitely."
The proposed closure of 6 Music, which has 695,000 listeners a week and costs £6m a year to run, has already sparked an outcry from celebrity fans including David Bowie and Lily Allen. A public consultation process is due to come to completion at the end of May.
Presenter Lauren Laverne and former Pulp frontman Cocker were recently named among the station's seven nominations for Sony Awards.
A BBC spokesman has described as speculation reports that the station is to be saved under a different name.
The prime minister told the Radio Times he was a fan of the "brilliant" US musical drama Glee, preferred Friends to The West Wing, and chose Lady Gaga over Madonna, and Cheryl Cole over Simon Cowell.
He also revealed that he had rung Cowell to ask him to come on board to help the national policy forum, but that the X Factor judge was too busy.
Source: The Grauniad