Mudguards are a definite, once on keep them there as they can be fiddly to remove and put back on.
Spare tights/socks or whatever you wear on your feet, keep them at work as if you get a real soaking no amount of footwear will keep your feet dry.
I use a rucksack with a dayglo water-proof cover, saves faffing about with panniers.
I suffer from cold hands, so along with water-proof cycling gloves I wear a pair of 'silk' undergloves - amazon sell them.
rechargeable lights, which get plugged in at work during the day.
A bell - pedestrians develop bicycle-blindness, especially if it's raining.
Spare inner-tubes, tyre levers, pump and multi-tool. A pair of 'disposable' vinyl gloves to keep your hands clean if you have to do any running repairs.
A final confession - I've never showered at work, even on the hottest day, have asked close work-friends if I was smelly and they've always said no.
.