layers are the secret to warmth!
merino wool offers a LOT of warmth for how lightweight it is. It's a great option if you need a base layer. As it is naturally anti microbial, it doesn't get smelly too quickly, so you should be able to get several wears per use before you need to wash. It will be more expensive than synthetic fibres, but you won't need as many of them so it soon balances out. If you can afford it, this is the best way to achieve warmth without bulk.
At the bulkier end of the scale, down jackets offer a lot of warmth and can look quite stylish. These come in lighter weight options all the way up to duvet style coats. Trespass often hit the style and low budget sweet spot without compromising too much on technical capabilities. TK Maxx will have lots of more fashion conscious options. Rab and North Face will have more expensive (and usually more technical) options, but there are bargains to be had if you are near designer outlets.
Go for longer line tops to ensure that your midriff is well covered. Keep your neck and chest covered too - either with a scarf, chunky snood or a buff (very warm for their weight). You lose most of your heat through your head so a hat is also a key bit of outdoors kit.
On the waterproof front, you usually do get what you pay for. Proper outdoor brands like berghaus, deuter, jack wolfskin etc will keep you much drier than a cheapy coat. They often offer hydrostatic head ratings to help you compare just how waterproof they are. Don't go anything lower than 2000 to keep the worst of the British weather out. The higher the number, the better the protection. Taped seams are also important to keep annoying trickles out. I like the option of adjustable waists, cuffs and neck guards to help keep the worst of the weather out and to create a more flattering silhouette. Another bonus of a really waterproof coat is that it helps keep the wind out, which again makes a big difference to how warm you feel.
Waterproof walking trousers are often very utilitarian rather than flattering. I prefer to use waterproof over trousers from berghaus. Mine were £20 on sale at the outlet. Poppers all own the legs mean you can easily put them on over chunky waking boots and they pack down into a drawstring case when I'm not using them, so they are easy to throw into my rucksack.
If you are on a tight budget, Mountain Warehouse is worth a look. Do bear in mind that their higher price items are often a similar price to sales offer on more technical outdoor brands. In my experience you do get what you pay for with outdoor kit, so it's worth the splurge if you know it is something you will get the use out of.