As a former Head of Music in an 11-18 mixed Comprehensive, I feel I have a little knowledge about peripatetic music lessons - these are where students are taught a variety of instruments by visiting peripatetic music teachers, who are not part of the school's main teaching staff.
There is no doubt that a lot of the teaching is excellent, of course. But there is always the added difficulty that students normally have to 'miss' something in order to fit their lessons within the normal school day, sometimes teachers are on courses, and occasional school holidays and closures can affect continuity. Furthermore the lessons are normally more expensive, as the school has to get its cut and/or they are not always individual one-to-one lessons.
The private instrumental teacher working at home can, of course, give a better overall service, except, of course, that the student then has to make their way to the teacher, and this normally out of school hours. The 'ideal', though in no way cheap answer, is to go to a dedicated Music School.
A good number of schools, and especially those in the private sector, are able to attract good private teachers, and many of their school websites confirm not only the excellent qualifications of the in-school music staff, but also of its visiting peripatetics. Not all schools, however are as lucky to have really well-qualified music staff - and, in terms of their visiting teachers, they don't choose to list them, or , if they do, their qualifications in their respective disciplines, are either conveniently left out - or they don't have any! In fact it's a sad state of affairs when someone advertises the fact that they are CRB-checked - as if this gives them the same claim to professional expertise as does some honest music qualifications.
It recently came to my attention, via a parent, that a student in a local school was asking for Jazz Piano lessons - something, apparently that was not available in school - or there was no flute teacher, for example, who could be persuaded to swap over and do the job as, sadly is often the case where peripatetics are not actually qualified in one area that they teach in.
I don't seek to blow my own trumpet (in any case, I'm a piano teacher!), but my name was suggested - I actually have a Jazz diploma, in addition to all my regular classical ones, and have had an excellent pass rate in Jazz, with many students gaining Distinction.
However, the teacher in charge at the school, apparently, when they were unable to come up with an in-school possibility, rather than suggest me, chose to find an ex-colleague/friend to do the job. I'm not bothered, as I realise that being well qualified can often be a disadvantage, especially when teachers can feel vulnerable because of their lack of such.
Don't be conned into thinking you'll get the best peripatetic teaching simply because it's on offer at a particular school - or that it's expensive! It has to be, as the school wants its cut, too!
And don't be afraid to ask around - word of mouth is still more important than any advert! The teacher in school is often biased, too, so an ABRSM or Trinity Guildhall local representative is often your best port of call for an honest appraisal!
PS If you're wondering what the piece of 'modern art' is above, it's actually a school shot, but suitably (hopefully!) disguised, so as not to give the game away!