My daughter is currently on the Rambert Pre Vocational course and loving it. She's just auditioned at London Studio Centre and about to an Rambert along with Northern Contemporary in Leeds. Like your daughter she's also 16. She's also in another youth dance company with other dancers at LSC. Both schools are good, in fact my daughter had a dance teacher who when training was offered a place at Rambert and LSC and she opted for LSC because of travel / location.
LSC fees are £16750 per year and you can get a £6k loan for fees, sadly not the full £9250 as LSC get their degrees validated through Middlesex University. I think the same may be true for Rambert. Their fees are £9250 per annum and it may be that the max you can get as a student loan for fees is £6k there too, as their degrees are validated by University of Kent.
It's worth remembering that both Rambert and LSC do 2 year Foundation Degrees first, with a 3rd year 'top-up' to a full BA. This means especially for 16 yrs old, they could do 2yrs at Rambert / LSC and then go elsewhere too since they are only 18 at that point. There are a number of dance schools that only take students from 18, e.g. London Contemporary - The Place.
Hope that helps.