OK, Tony, I understand where you're coming from, mine looked like that when I started last summer. I have ME/CFS, so what I can do is limited. How I tackle it is:
1 Buy decent gloves. Mine are the gold leaf tough touch ones, and, apart from the seams are bramble-proof. You will need them as brambles, even when dead, are bloody lethal.
2. Doesn't really matter what you use to chop it down, I have trusty loppers and secatuers for chopping up the brambles, green bits go in the council green bin, dead woody bits go in dustbin incinerator type thing (aldi, £20 ish). Chop down all stuff to about 6 ins/1ft.
3. Dig out brambles. They only go down a spade and a half, so aren't difficult to do. If you have any other weeds, like bindweed, these are a different matter.
4. Anything that dares poke it's head up after a week, use roundup or something similar. Keep spraying, it will eventually get the message and turn it's roots up and die.
5. For both yours and your Mums' sake, once that's done, put down weed supressing membrane, and cover with something like pea gravel. It will look a lot nicer, I'm sure I'd be depressed looking out at that lot, and pea gravel might not be every one's choice, it's better, far better than what's there now. The council can and do fine people (even if you own the house) for letting their gardens get out of hand, it only takes the next door neighbour one phone call to the council/councillor and they can get stroppy with your Mum - I wouldn't want that for anyone, especially not my Mum.
To answer your question, weedkiller takes between 4 and 6 weeks, and it needs to be dry for at least 4 hours after you spray it on, maybe more. If you want instant improvement, go the gloves and loppers route, if you're lazy and/or have the time and money, then go down the weedkillers route.
Brambles only go down a spade and a half, so are quite easy to dig out, BUT, the tiniest bit of root will re-grow.
Once you've done it, please use the weed membrane and pea gravel, and then you won't have to do it again in a couple of years. And a couple of years after that.
Your Mum should also be a lot happier and won't be nagging you to do something about that wilderness. Very depressing.