Going slightly off topic but touching on some of the earlier posts... from a music teacher's perspective I wish that schools would offer general musicianship courses for ALL children to teach the fundamentals of pitch, reading music, beat, rhythm etc before embarking on concentrating on a specific instrument. Unless the child concerned has an extraordinary talent or has shown very early promise, starting to learn an instrument in reception can be completely counter-productive.
The concentration required, the skills required, combined with the repetitiveness of learning an instrument can be very negative for 4 or 5 year old, and sometimes they're really not ready for it until the child is much older. There are many more fun ways of encouraging music making that enable children to learn the basics before moving onto learning a specific instrument when they're more physically and mentally capable of doing so.
I wish that all state schools had the funding and expertise available to have all KS1 children learning along the lines of Kodaly and Orff, using the voice as a instrument and tuned percussion and then graduate onto more skilled instruments. Even learning the recorder or the ukulele are useful stepping stones and really should be much more encouraged.
However, rant over and back to OP
Prices seem to be in line with what I would expect to pay for peripatetic tuition at my DCs school. However, I would pursue private tuition, which may not cost much more and give you the benefit of being able to find someone who will suit your child and their way of learning.