I suggest you try a private message to Anchorman and ask what the best way is to deal with these weeds.

Hi jlbraders, welcome to Goy. When you say the membrane didn't do its job, do you mean the weeds were growing through it, or is it seedlings growing in the gravel, If the membrane failed, It was maybe poor quality, so you could replace with a better quality product, giving you the chance to remove any roots of weeds still present. As for seedlings growing in the gravel, this is a problem for me also, it is a perfect environment for seeds to germinate readily, I find regular raking helps, and of course the old manual weeding technique!

You've mentioned bracken - that will come through a membrane, unless its a very thick, heavy duty one, and even then, might still appear. Bracken is really, really difficult to get rid of, I haven't yet found a way of killing the blasted stuff off. Nettles should be possible to dig out, but their roots are extensive and go quite deep, so if they've reappeared, it may be that you didn't get out all the root. small weeds, as Dido says, will germinate and grow in the gravel, because soil inevitably collects amongst it.
If you don't want to plant in the gravel, I'd remove the existing gravel and membrane, dig out as much as possible anything that's there, and apply something like sodium chlorate to the area (if its still available, I have a feeling its been withdrawn, or will be shortly), then lay the best quality membrane you can find, not just the cheap weed fabric, and replace the gravel -which should be 2 inches deep really. Thereafter, it may be necessary to apply path weedkiller, something like Pathclear, in about April each year.

Nettles are easily killed with Roundup. One spraying usually does the trick but occasionally two are necessary.

If you use sodium Chlorate you will not be able to grow anything in that area for a long time(OK if you're just covering with gravel but not OK if you want to plant new plants through the gravel.

I have no experience with killing ferns/bracken but I guess SBK brushwood killer would work as it will kill brambles,thistles and tree stumps!

Sodium chlorate can also damage adjacent shrubs and trees.