I have a patch that gets overgrown with brambles - currently I chop them down with a strimmer, but wonder if there is a more permanent solution? One of my neighbours has covered his with a thick black membrane… but I imagine this could take a year or two 
Are there any quicker (and permanent) fixes?
Yes, you have remove the roots. This involves digging right down into the root system and lifting the entire thing and binning it. Try not to leave any broken roots behind because it will take hold again.
Its how I got rid of my old bramble bush (which I moved to another spot in the garden)
Not sure what the black membrane is?
Totally agree the only way is dig to dig out as much of the root as you can DO NOT compost them
Cut them back to near the ground then paint the freshly cut stalks with neat Glyphosate 360 (Roundup if you can’t get the cheap Chinese stuff).
Might take a couple of goes if they are persistent like Wisteria or bamboo. But that will definitely do the job and involves a lot less digging.
Thanks for the tips everyone. I think part of the issue is that right at the back of the garden (where they are) we dumped a lot of rubble there (all the old brick walls when we remodelled the house) part of this is to help with flood defences (there’s a river at the end) and part of it is because this is what many other neighbours have done (it also saved on a load of skips 
)
So being able to pull the weeds out will be difficult, hence thinking about the membrane, and as much as I hate using Glyphosate and other chemicals, considering that avenue. I did hear someone once say burning them might work - but kids are always starting fires up the mountain and they seem to grow back every year!
I wonder if you could lay chicken wire across the area and guide the brambles through it? The flowers are lovely, and the actual brambles are very tasty! Plus if you curtailed it along the ground (those tendrils can be quite long and prickly), it would make a nice edging between the end of the garden and the river (also add to the defenses, hide the wall rubble, etc…)
Flamethrower. 
I’ve heard that before SM… does it kill the roots tho?
Glyphosate 
Okay, it’s not nice but I think it’ll do the job!
Actually I did have a mini flamethrower for the garden some years back. I found it more useful for lighting reluctant barbecues without burning the fingers rather than the horticultural stuff! 
SPK weedkiller on new shoots after you’ve cut it back
Coincidentally the High Court has just thrown out a class action against Roundup and Monsanto (Bayer)
