This information is not held centrally.
However, in 1999, 2002, 2005 and 2007, the Department commissioned surveys of local authority music services, which collected data on the prevalence of music tuition. Survey reports are available at:
http://www.dfes.gov.uk/research/programmeofresearch/projectinformation.cfm?projected=15161&keyword=music%20services &keywordlist1=Local%20authorities&keywordlist2=Arts&keywordlist3 =0&andor=or&type=0&resultspage=1
These are national data rather than broken down by local authority, but they provide an indication of the music tuition that children and young people are receiving.