The only hint that this tall, well-proportioned woman is controller of BBC Radio 2 is her Sony earphones: she is listening to Terry Wogan, whom she brought back to the network last year.
This is the manager who pulls the strings at the BBC's most consistently successful radio station, controlling the professional lives of some of Britain's best-known radio personalities.
She has also quietly turned around Radio 2 to capture a confident 13.4 per cent share of national radio listeners. In the BBC's annual report last week, the network was praised for maintaining its share last year despite increased competition, and for persuading older listeners to stay tuned longer.
Ms Line has earned a BBC car but she commutes on public transport because she likes to keep in touch with her audience. 'I am able to represent the listeners because I am one of them,' she says. 'Although I came from Radio 4, I would naturally tune to Radio 2. I am not someone with degrees and a high intellect.
'I am not suggesting that the people who listen are stupid, but I am not a graduate. I am in my fifties, which is the audience age group we are aiming at.'
With the air of a head girl proud of her school, she points out the photographs of Radio 2's award- winning team on the wall opposite. Colleagues speak of her with affection - the personal touches such as birthday cards for her staff, handwritten notes whenever a good job is done, straight talking if the news is bad.
But this bank manager's daughter has a bit of steel in a character refined in a broadcasting career spanning 37 years. She arrived as a clerk typist with six GCEs, a swimming certificate and the gall to tell her interviewer of her ambitions to become a producer. In the five years since her Radio 2 appointment, her strong popular music policy has rid the network of its derisory 'Radio one-and-a-half' tag, and her programme planning has paid off in audience loyalty.
'I just went in there to make Radio 2 as good as I possibly could, and the top station,' she says. 'I suppose more because other people are juggling about at the moment in their own difficulties in other networks, we are really coming through. Our day has come. I have always felt we are kind of underrated. It is rather lovely to find that at long last we are being recognised and applauded.'
Ms Line sounds practical and calm as she uses shopping-bag metaphors to explain how she picks up a prized presenter or two. 'I just look for people I would like to hear, and try to assemble them in the right order.
'You can have a long-term aspiration that you would like to get X or Y, but I have been fortunate in being able to persuade Terry Wogan back and to get Michael Aspel on Sunday mornings. These two were certainly on my shopping list, but you can't always get them, not because you are not doing your stuff but because people are not available.'
She is not one for passionate speeches. Her voice is deep, quietly confident, chatty yet controlled, and she happily makes a joke at her chunky-sized body's expense. Asked if she had taken part in a recent BBC 2 get-fit initiative, she counters: 'Do I look as if I have?' Her husband, Jim Lloyd, who presents Wednesday's Folk on Two, is the athletic one. 'He is the great walker, while I stay behind to watch the EastEnders omnibus. I hate the word workaholic, but I am certainly wedded to my work.'
Frances has two grown-up step-children. 'Jim was not looking to have more, and I am not a maternal sort of person,' she says. 'I like kids but in small doses.'
Her programme planning is diverse: plenty of music, an arts programme three times a week, and reports and discussion of social issues. She moved Derek Jameson from the breakfast show to a late- night slot with his wife, Ellen, four times a week; introduced Brian Hayes's weekly phone-in current affairs programme, Hayes over Britain, and his slots on Saturday and Sunday; and brought in the Radio 2 Young Musician of the Year competition, the Radio 2 lecture and a series of eight musicals such as Guys and Dolls and Salad Days.
'In the same way that Radio 3 is the home of the opera, we have consciously decided that Radio 2 is to be the home of the musical,' says Ms Lines. 'This is a development I think the listeners will really like. We won't be doing anything obscure. It will be all the established favourites.'
More than 9 million people a day tune to Radio 2: a 'grey power' audience with deep pockets that commercial stations would love to attract.
'One would be silly not to be nervous of the opposition, because some of it is extremely good,' she says. 'But we have actually targeted the over-fifties. It is a growing audience, and I am fairly confident they will stay with us. The median age of the audience is 61 and they listen for long periods, very faithfully.
'All you can do is believe in your product: that it is right for the audience you are aiming for. You are always most vulnerable in the middle ground. I don't so much fear the niche broadcasters such as Jazz FM, because I don't think they take away our listeners. Our great strength is the breadth of output, and, of course, the combination of speech, the terrific personalities and the music.
'I am looking for all sorts of listeners. One of the great problems is trying to stop people thinking that they have to be in a wheelchair or on a Zimmer-frame to listen to Radio 2. It is not so. I am trying to get some radio pride going.'