Re:
...Anything with PU waterproofing will be very, very sweaty
...Anything with a membrane (Goretex etc) will be sweaty one it starts raining This is because the pored membrane that makes them theorrtically unsweaty relies on moisture density gradeient diffusion - ie they need to have dry air on the outside to get rid of sweat, which is a bit of a flawed concept for rain gear.
...Paramo rain shells aren't sweaty (they have a liner that sucks water out of the shell) but they're expensive and have too much insulation for year round use. eVent is also better than Goretex, but out of your price range, and Polartec Neoshell is said to be brilliant but is even more expensive.
Your best option is a pertex windbreaker treated with Nikwax. Nikwax is water repellant gunk that can make even denim reasonably rain resistant. A Paramo Fuerra Ascent would probably do what you want better than anything else. Pertext is windproof, but almost as breathable as cotton, and the Nikwax will stop it wetting out. On your budget, it's probably the best option. If you go for the smock version of the Fuerra instead (no zip) then it will fold to go in your pocket. (If you do this then read up online on how to use Nikwax and follow the instructions exactly!) But any reasonably made pertex shell will do as long as it isn't PUed and doesn't have a membrane layer.
Useful:
http://www.gooutdoors.co.uk/expert-advi ... rproofing-
You can also use Nikwax - there's a different type for each material on jumpers, fleeces, trousers, etc. So you can have a rain resistant layer under your shell - ideally of a material that's warm while wet, like wool.
Oh - you can sometimes find Paramo seconds on ebay. In case which the Velez Adventure Light is the want you want for winter MTBing - it's so good that it's almost unbelieveable. It would probably still be more than £100, but your can clean and re-proof in a washing machine, sew up tears (unlike a membrane shell.) People reckon a 10 year life is about right for one. It has the best hood for cycling I've used too. Just don't buy oneif you're not good at following instructions, because it needs regular (every few months) re-proofings in a washing machine and if you mess this up you'll be soaked!