Based in London, the centre includes an extensive library of printed music, which it lends to schools, choirs and youth orchestras. It also provides musical instrument tuition for secondary pupils.
The centre, which forms part of Trinity College of Music, was founded by London county council. After the demise of the Inner London Education Authority, responsibility was transferred to Trinity College.
The centre has been housed in temporary sites around Greenwich. The college said it cannot afford to rent other premises.
Paul Flynn, Labour MP, has tabled an early-day motion in Parliament, calling for the centre to be preserved. He is supported by more than 50 MPs.