"Conservatoires are a bit snooty about brass bands," he comments. Although a professional trumpet player, he could never be called an elitist.
Mr Henderson, who is chairman of the Youth Music Trust, set up by the Government last May to boost instrumental teaching, explained that only in the past 70 years has the wide distinction grown between people making their own music - singing round the piano, dancing round the maypole - and top performers.
The trust won't make that distinction, he promises. "It must not be confused with the search for a second Jacqueline du Pre, although it will provide the opportunity for fine talent to emerge. But it is fundamentally about making music a central part of everyone's life.
"The human frame is made for music," he says. "We all have volume control and pitch."
His passion for ending snobbery in music is shown by his lifelong involvement with the festival world and with the Dartington summer school since the mid-1980s. Dartington, where professional and amateur musicians work together, provides an ideal model for the trust's work, he says.
The YMT, set up by the Government with pound;30 million from the National Lottery, last week announced the appointment of Christina Coker, founder-director of Hackney Music Development Trust, as its first chief executive. A "phenomenal 120" applied for the top post; the trustees wanted "someone from the educational side of the performing arts world, not the performance side of the educational world," said Henderson.
The trustees' meeting next Monday will decide on up to 20 trial projects from a range of genres, with wide geographical and social spread. "The trust is not an adjunct of the graded instrumental exam system. It is likely to support inspiring eccentrics - animateurs - rather thaninstitutions."
The money will definitely not replace cash for local authorities which decide not to use Department for Education and Employment Standards Fund money to support music services, Henderson said firmly.
Although unstinting in his praise for Education and Heritage secretaries David Blunkett and Chris Smith for their "refreshing attitude" towards music and the arts, he is anxious to underscore the independence of the trust. "We mustn't be a tool of national government."
The trust, which has just been renamed the National Foundation for Youth Music, (the Charity Commissioners thought the original name too close to other organisations), will act as a "kind of sub-post office" for the National Lottery, he explained, distributing pound;30 million from the Arts Council Lottery Fund over three years.
Apart from that part-time post, Henderson has the kind of curriculum vitae that makes you want a lie-down. Not only is he principal of one of the leading conservatoires, and artistic director of Dartington International Summer School, but he's also a member of several arts associations, governor of Brighton University and Chetham's School, Manchester, and a writer and broadcaster.
His capacity for work and leisure are legion. He still finds time to play the trumpet: his latest public appearance was last month at his club, the Savile, just down the street from where Handel wrote The Messiah in 25 days. Music runs in the family; one of his two sons, Piers, joined him on the trumpet.
"The Savile was my university; that reminds me of Osbert Lancaster, who said his education took place between terms at Eton. I joined as a student when I was 18 and learned at the dinner table from a wonderful variety of musicians and artists," he grins.
His formal education was at Brighton College, the independent school where his father taught, Brighton and Kingston art colleges, and the Slade School of Fine Art.
Education plays an important part in the life of Trinity. It is the first conservatoire to set up a post-graduate certificate in education course, starting in September, with the London Institute of Education. The college has a continuing education department and runs an MA course to prepare graduates for work in the community. He believes that conservatoires should become more involved in teaching, a view not shared by all.
Apart from musical pursuits, Henderson enjoys cooking seafood - "I was taught by a wonderful French cook in Dinard, which came from years of going over to Dieppe on the ferry from Newhaven." The port is not far from his Brighton home; and he used to be "passionate" about hill-climbs in vintage cars.
That passion is now confined to "tearing around the Devon lanes in a blue two-seater replica Type 35 Bugatti". He also fights for the survival of seaside piers by presiding over the National Piers Society, which is "full of eccentrics - scientists, artists, as well as train-spotters".
His next major task is to complete the college's plan to move from its cramped Marylebone buildings to the Royal Naval College in Greenwich, south London: "It should happen in 2002." By that time, he will probably be moving on to pastures new.
Larry Westland, chief executive of the charity Music for Youth, summed up the thoughts of many who know Henderson: "For me, Gavin has always been a larger-than-life character. Goodness knows when he sleeps."