We had same problem and sorted it by cutting down all brambles and other overgrown stuff with a powerful hedge trimmer - the bonfire burnt for 4 days - and then digging over an area at a time deeply. and havingmore bonfires. Some areas I sprayed with Roundup plus but have found roots still need to be dug.Ihn fact our bonfires became a joke with our neighbours!
We then kept them cut dwon in areas we were not working on and have slowly beaten the stuff. In the cultivated areas we still have weak brambles but are easily sorted. You do have to keep going over what has been dug.
21/2 years on we still have areas to 'un-bramble' in fact I have started on the last bad area today.
I don't think there is a quick fix really, just hard and persistant work.
Now in the area started today i have found a few (4) newts under some builders plastic. Replaced plastic for now but does anyone out there in garden land know where I can put them without harm, blue builders plastic is right where new rhubarb bed will go