Patience appears to be the best approach. I have a 'clearing' (about 3000 sq m) in my woodland that was covered in bracken (to a height of 2m+, and to the extent nothing grew underneath). Over the years I've been breaking the tops off the stems as they come up - it's now very much weaker, and grass and heather are flourishing.
Depending on what else you do agriculturally, you may also consider making use of the bracken that does grow. I rake up a lot of the dry stuff every year - I use it: as bedding for my hens (apparently bracken was extensively used for animal bedding in the past because it is much more absorbent than straw); as a mulch on my allotment, where it does a fantastic job of keeping moisture in the soil; and as a soil conditioner in my greenhouse, where it breaks down to provide a rich, friable growing medium (it's slightly acidic, so is well suited to blueberries and strawberries, and my tomatoes and cucumbers seem to do pretty well in it)
I also intend to try letting a couple of very large piles rot down - I understand the well-rotted bracken makes a good seed and potting compost.
None of the agrochemical control techniques are benign from a wider environmental perspective. Even if you keep the glyphosate on the crop and it breaks down into harmless compounds in the soil, the manufacture of it is energy and resource intensive.
I'm assuming that, since this is the SMALL WOODLANDS Owners Group, you're woodland isn't a large commercial enterprise. Given that, is it important that you eradicate all your bracken RIGHT NOW?! Tackle it slowly, and encourage the woodland to encroach on the bracken-infested area - bracken grows very poorly, if at all, under the canopy.