I did not read the letter that this letter refers to.
I do not know what a "flute band" is, as defined by someone living (and playing!) in the UK.
I have no idea what kind of specific behavior rankled people so much that they "ridicule and complain" about the so-called "flute bands," however, I will say that it kind of sounds like fun.
Enjoy: http://www.newsletter.co.uk/community/letters/flute_bands_liven_up_parades_1_3061269