I know of a couple in the west midlands, Try Lorna at training midwest ltd 01452780418, Peter Harmer 01905381081, most rural and agricultural colleges run courses as do the small woods association.
If your felling on your own land it's up to you if you get a ticket or not, but I'd strongly recommend you do. If your paying for the training you may as well take the assesment, it gives you and others the confidence of knowing your trained to a standard. If you work on other land, or want to be insured you'll need it.
LANTRA provide the training and a cetificate of competence, NPTC do the assesments.
There is funding available for 50% of costs if you work in forestry.
Much as I think training and certificates is a good thing it's also a pain, to use our forwarding trailer and tractor on forestry commission land we both need to take FM03 and extraction by skidder at the end of the month, which is a little expensive, as well as needing a loler.
And folks complain about the price of wood.