I'm a Glasgow runner and the shoddy weather is really setting in now. I have a heavy-duty coat but I'd boil alive in it if I attempted running in it! Even if I wanted to just belt off into the rain I run on a bit of a tight schedule.
I'm on a modest budget too but if it's not too extortionate I can save up a bit more money if the investment will be worthwhile. Feel free to share any alternative suggestions too. 
Hi.
I honestly don't mind getting wet as it cools me down a treat, so dont mind running in the rain. My one piece of essential kit is a cap with a big peak to keep rain out of my eyes.
I have got a showerproof/windproof jacket which I bought (not cheap) from a running shop in early spring but to be honest I take it off once I have warmed up, as I get so hot!
I think you might have to spend a lot of money to get a jacket that is breathable but truly waterproof? On the other hand, it seems from other posts that Aldi are doing great running stuff so if you are any where near an Aldi, run on down there before they run out (?) (I dont have one near me).
Hi, mcb, I bought a lovely bright pink waterproof jacket (matches my face after 10 mins or so!) from Sports Direct for £19.99. I've used it for cycling but not running yet but it seems okay. I also got a running/cycling jacket from Lidl for £12 or so. It's not waterproof but is showerproof and it has a nice warm lining so might shield you from some of the colder Scottish winter weather.
Running in the rain is never as bad as you think it is going to be. I've tried running in an old Berghaus but actually prefer just to get wet.
I think the key thing is to warm up quickly and get moving then when you finish make sure you don't loose heat by adding a layer or if going for a shower if that's possible.
Hi mcb I'm Aberdeen so I know what bad weather is we get loads of it up here. Sports Direct sell a HiViz Karrimor jacket yellow or pink which I used last winter and found kept the wind out perfectly well, quite good for the rain and sleet up to a point. To be honest you would have to spend about £200 or even more on a good Fell Running jacket that would be waterproof but what you need when running is something that lets your body breath or if your any thing like me you will overheat even in the cold weather. Getting too hot saps your energy very quickly.
A cap is great for keeping the rain off, also good for keeping the sun off too Huh!! Also gloves I find are a must, just a light weight pair, Aldi have smashing ones for £2.99 just now, but SD will also have. Happy shopping and running.
If you can get to an Aldi the running jackets are quite nice - cut on the small side though - the large is described as 16-18 but I'd say more like a 14; ditto the long sleeve running top.
I was similarly worried about the rain - but now realise that people on here are right - getting wet is no problem. Being cold is. So I find that having a top with long sleeves, running gloves and a hat are essential.
