would have thought there are plenty of state educated pupils that play an instrument to a high standard.
Not any more.
State school children historically relied on LEA-employed instrumental music teachers, known colloquially as "peris" because they were peripatetic, travelling from school to school to teach. A lot of state school kids' parents simply can't afford the cost of a private teacher.
Funding cuts to local govt, combined with an increase in academies aka "school privatisation", means that LEAs often can't afford to run a peripatetic music service, or if they do, they can't provide that service in the academies because they can't provision LEA services to non-LEA-funded schools. It's up to the academies to decide whether to offer in-school instrumental tuition and they set the cost, which is likely to be more than the LEA would have charged.
In the last forty years, looking just at the LEA I had when growing up, the peripatetic music provision has gone from free lessons with free instrument loan for the first six months and free Saturday morning music centres, to £150/year for lessons, waived if parents were on means-tested benefits, with the Saturday centre included, to £300/year, to complete withdrawal of the service. I'm aware of an international-level soloist who learned through my LEA. There will be no more international-level soloists learning through that LEA.
I started lessons when it was free and remember when the £50/term came in. Peers stopped lessons because parents wouldn't or couldn't pay. It's important to keep in mind that there are parents who refuse to pay for extra-curriculars despite having the means to do so. Blanket free provision allows the children of those parents to take part.
I play in a very niche competitive type of musical ensemble and we have our own news websites and forums. A constant refrain on the forums is recruitment trouble and ensembles closing down because of lack of players. I was in an ensemble that was over 100 years old when it folded. We are absolutely seeing recruitment problems because kids are not learning instruments, and we are seeing them even in the upper echelons of the competition structure.
At a recent conference for the players of my instrument, the conservatoire students were all plum-voiced, well-heeled, with many talking about their time at Chethams. Twenty-five years ago, you'd have heard northern accents in the mix and discussions of their holiday jobs. State school children are being priced out of playing and I'm not in the least surprised that it's starting to affect university intakes.