Posted: Yesterday at 21:22
Best thing you can do is get it all strimmed down right now. Apply a glyphosate based weed killer and let that work for a few weeks. You won't get the best out of the weed killer as it's late in the season, but for now its the best option. personally I'd then wait till spring when the weeds are just coming up and then tackle it again with weed killer. If you try and put down membrane, even top quality landscaping membrane, down now, weeds will come through next spring and I've seen nettle lift membrane before and it's a hell of a job to get it out.
In spring spray at two weekly intervals for a month, leave a further two weeks and only then can you really think of laying a membrane and putting slate chips on top.
It may not be what you want right now, but in my experience it's worth the wait. Impatience can cost money in the long run.