Very occasional use of Roundup on areas where you're not growing edible plants is fine, just don't breath in the spray or get it on your skin.

That said, Roundup's not going to do much, especially at this time of year. It won't kill brambles, but will kill soft weeds, provided they're growing strongly. It also has no deterrent effect on regrowth - you'd be better off using something like Bayer's Ground Clear which does prevent regrowth for up to 3-6 months, intended for use on uncultivated land, though its unlikely that will completely kill well established, woody brambles either. Best applied in spring when things are growing strongly, but it should do something even now.

yes I agree with what bamboo says re weedkillers.

I agree with the others, but what about clearing the brambles then leaving it as a wildlife area?