英國和香港的學校

是, 英國和香港的學校都是在9月開學, however, for secondary schools (boarding schools) hk only have two academic terms in a year, UK has 3: September - December, Jan - mid or late March, April - early July.
For Further Educations, will have two terms, as usual.
英國有學校主讀音樂
The most famous one would be Royal Academy of Music
圖片參考：http://www.ram.ac.uk/ram/gfx/logo.gif
(= 英國皇家音樂學院 - www.ram.ac.uk/)
The Royal Academy of Music (RAM) is a constituent college of the University of London, and is one of the leading music institutions in the world. The Academy has students from over 50 countries, follow diverse programmes including instrumental performance, conducting, composition, jazz, musical theatre and Opera. Academy students perform regularly in the Academy's concert venues, and also nationally and internationally under such conductors as Sir Colin Davis, Yan Pascal Tortelier, Christoph von Dohnányi, Sir Charles Mackerras, James MacMillan and Trevor Pinnock.

Yes, both HK and UK schools start their first term in September and UK students also enjoy a nearly half school days-half holiday system. They get half terms and end of terms holidays, each thrice a year. some schools, like mine, even have half days on alternative days.
There should be schools which are very good at music but the probability of having a school which ONLY studies music is rare, apart from the Royal Music School (or something like that), but you have to be extremely good to get in that school.