You have my commiserations, I'm in the same boat, and posted a similar thread a few weeks ago to see if there was a miracle cure. Unfortunately you are in for a LOT of hard work.
The general consensus of opinions is the best way is to chop off the top growth and then dig out the roots, that's the only way you will get rid of them. Come spring, when the dratted things start actively growing again, you can spray them with glyphosate, wait for them to die & dry out, and burn the new growth (in a suitable dustbin type incinerator, otherwise you risk burning your entire garden, plus neighbours fences, which won't make you very popular! Then it's down to digging out the roots, I'm afraid.
Invest in some decent gloves, and wear a close-fitting jumper to protect your arms (loose and you'll get tangled by thorns). I find the easiest way of dealing with them is to take some telescopic loppers and chop the buggers off about an inch above ground (so I can see where to dig), drag out the resulting growth, chop it into two-foot lengths and feed it to my dusbin burner. I'm disabled and have two small children, so you will probably finish clearing before me. It's strangely theraputic though, and you will see a (small) difference after a couple of hours. I hate brambles, even when dead the dratted things can still draw blood (make sure your tetanus is up to date!).
When I find time I will post some photos of progress. The entire back garden still looks like something out of Jurassic Park!