"I was convinced we were about to be taken off air," Laverne said.
"In a strange way the threat of closure has completely turned things around for us because not only did our listeners step in and save us by complaining to the BBC Trust, but a lot of people who didn't know we existed found out about us."
She added: "Our listening figures doubled and are rising all the time now, which is really exciting.
"It's a brilliant place to work. As long as there isn't a lot of swearing in a song, we can play what we want. There's a lot of freedom, which is really important for me."