To answer your actual question, Ian, I recently used Tewkesbury Saws. Email Dawn Hardy, DHardy@tewkesburysaw.co.uk
and was very satisfied with the four I had done. Their quote was:
"For a standard sharpen & set price will be £11.77 + Vat each, without seeing the blades any additional work will have to be quoted for. If you have 10 or more we can offer you less 20% off the price." Plus postage of course.
I had two rip, one tenon and one gentleman's saw done, down to 14 tpi. I am not sure if they do finer, but ask, and they only do rip cut, not flame.
I preferred to pay someone expert rather than acquire the equipment and the skills and spend the time to get a whole-decent job done!