The Independent Schools Council offers advice on School Fee Assistance with several links to scholarships and bursaries available to pupils being educated within the Independent Schools sector as well as Government grants, Local Authority grants and grant giving Trusts.
If you are looking for other sources for independent school education funding, the Educational Trust's Forum is a list of Trusts specifically funding private education and boarding and is an excellent starting point. They may or may not help you with funding dance education specifically but have a look at the criteria for applying to each Trust to see if it is suitable for you.