I'm a bit surprised no one has mentioned the excellent degree programme in Scots music which has now been underway at the RSAMD in Glasgow for some 6 or 7 years. Many of the graduates are acknowledged as very fine performers despite (in some cases) their youth (Emily Smith et al). The lecturers are among the finest of the 'revivalists'(including Alison McMorland and Pete Clark)- as for the examiners I cannot comment as I was one for 4 years. The programme is led by Brian McNeill, which also says something for its quality.
Then there is the Traditional Music Centre of Excellence at Plockton High School led by Dougie Pincock - this acts as something of a feeder to the RSAMD Degree.
As for England, I hear good reports of the programme at Newcastle University run in conjunction with Folkworks.