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Copyright in music lasts for 70 years from the date of death of the composer, or the last surviving collaborator for a co-written work. Copyright protects the reproduction of the printed music manuscript/notation (whether in analogue or digital form) as well as the music as it is recorded or performed.
Fair dealing exceptions are difficult to apply to music as the definition of what is a substantial level of copying can rarely be linked solely to the length of the musical section being used. As of 1 June 2014 copying of sheet music is now legal for the purposes of instruction (S32). However the copying must be fair so is unlikely to extend to making copies of whole works for music examinations if they are already made commercially available for that purpose.
Whilst the exception allowing performance of copyright works for educational purposes (S34) will usually cover performance of music at closed teaching events, permission to publicly perform or reproduce music is usually covered in the UK by PRS for Music who have a range of licensing schemes. However it may be necessary to contact the music publisher(s) or composer(s) directly if your intended usage is not covered by an available licence, or the rights holder is not a PRS for Music member. You should also be aware that the rights in sound recordings are distinct from the rights in musical works so you may need to seek multiple permissions if you are using recorded music.