Not Leeds but there is the Yehudi Menuhin school in Cobham, Surrey which is an independent boarding school with fee support from the "music and dance" scheme from DOE.
DoE website says this this about the scheme and lists 5 music schools nationally:
History of the Music and Dance Scheme
Before 1973, support for pupils at schools such as those currently in MDS schools was provided by local education authorities under discretionary powers provided in Sections 55 and 81 of the 1944 Education Act. In 1973, the Royal Ballet (Lower) School and the Yehudi Menuhin School were admitted to a fee remission scheme funded by the Department in recognition of their position as Centres of Excellence for the Performing Arts. The fee remission income scale (i.e. the means-test of parents) mirrored that of the old direct grant grammar school scheme with some modification to account for the higher costs of boarding and specialist tuition.
The Gulbenkian Report (1978) on training musicians reviewed the state of specialist music education. It was largely as a result of the recommendations in the report that the Music and Ballet Schools Scheme (MBS) was set up in 1981.
Five specialist music schools in the UK were designated: Chetham's School of Music, Wells Cathedral School, Purcell School, Yehudi Menuhin School and St Mary's Music School (Edinburgh). Together with the Royal Ballet School, lower and upper divisions, they were allocated Government-aided places under the Education (Grant) (Music and Ballet Schools) Regulations 1980 SI 1980/684 (or the Scottish equivalent).
The scheme was expanded in 1996 by the admission of two new schools (Elmhurst School for Dance and Performing Arts and the Arts Educational School, Tring), and with extra places at existing schools. In 2002, the scheme was renamed the Music and Dance Scheme and another dance school, the Hammond School, Chester, was admitted (from September 2002). Since 2004, the scheme has broadened to include newly designated Centres for Advanced Training that provide out-of-school-hours training and learning opportunities for many more talented children.
