To me, the first photo looks more like pyracantha and the second more like bramble. As it is an overgrown area, it could well be a planted pyracantha where some bramble has sown itself.
I have pyracantha near the house (planted by previous owners as a deterrent to climbing the fence) and lots of bramble around the garden. Brambles are almost impossible to eradicate w/o using a herbicide repeatedly or by digging up & removing a lot of soil as they regrow from roots.
My pyracantha had been left alone for too long (5+ years) before I tackled it early last year and it was much bigger (well over 20' in places) but a mate & I tidied it up in a day with secateurs, loppers and occasionally a saw - some parts were 4-5" thick.
When doing that I wore ordinary leather gardening gloves as we mostly were cutting off branches and so could hold them by non-thorny parts.
Before shredding everything I bought a pair of these
https://www.screwfix.com/p/stanley-split-cowhide-leather-driver-gloves-brown-large/23256
which gave better protection but still I ended up with loads of tiny pin-pricks on my hands. So personally I would look into welding gloves before doing this again.
Brambles I just cut off any long runners with secateurs and then dig up to remove as much root as possible. I always cut off the root ball from brambles before shredding to avoid getting stones / grit in my shredder.
It is very late in the year to be significantly cutting a pyracantha, birds may be nesting now. That sort of work s/b done October to February.
In your position I would take off some of the lowest parts that are sticking out (e.g. up to waist height) to create access to the ground so that you can get rid of as many brambles as possible. When, not if, the brambles come back let them get several inches high with plenty of greenery and spray with a glyphosate herbicide. You must spray the leaves as that is how glyphosate is absorbed, it is then translocated to the roots and kills the plant. That takes a couple of weeks. You may well need to treat brambles again later in the year. As I said they are very persistent.
When getting close to pyracantha make sure that you wear eye-protection. The thorns are wicked, the branches are twisty and springy.