I commuted ~10 miles each way in Dublin for a couple of years. I was lucky in that I was a grad student - there was no expectation on me to look presentable
. In my experience, you're going to get wet far more often than you're going to get cold. Keeping the rain off, and the subsequent wind chill is key, because it doesn't really get
that cold. As someone already mentioned - to calibrate, wear enough that you're a little chilly starting out - if you're comfortable setting out, you're going to be overheating 15 minutes later. I also found that you're never going to stay fully dry - you can only hope to avoid getting completely hosed. Even a decent rain cape will let water in at the neck opening, but hopefully just enough to be annoying. But a cape will allow air to circulate under, which should reduce overheating. Fancy "breathable" waterproofs will have you sweating in no time.
I would say:
Fenders - essential
Cape - also highly visible!
Rain pants
Woolen hat
Some sort of fleece or woolen sweater - I had an old
bainin (white Aran sweater for our US cousins) that I reserved for cycling - even if it got wet, it still did the job
waterproofish gloves - neoprene is good. I used fingered gloves - it's not cold enough to warrant mitts.
Some sort of overshoes, because your feet are going to get soaked. I just carried my actual shoes & socks in my backpack and let my trainers get soaked - which they did.