Here’s what I’d take as a minimum, taking into account that it’s Wales so might rain.
Sleeping bag … I spent a night out last week in a cheap, +10 synthetic bag and didn’t die.
Bivvy bag … Something like an AlpKit Hunka will be fine.
Sleeping mat … Cheap foam mat from somewhere like Field and Trek will cost under a fiver and won’t weigh much.
Polythene dust sheet … as a tarp it’ll last a couple of nights without any trouble. You’ll obviously need a set of cheap pegs and some cord. There’s some stuff on the WRT blog about attaching guys to the poly.
Sleeping bag, wrapped in bivvy bag, all tucked up inside a dry bag and strapped to the bars.
Add in a warmish top to kip in, a bit of food and some spare socks and you’ll not die.