Got the new part, took the old one off and sure enough, a pretty long crack on the inside and outside:
Put the new one on, filled up the water, and hey presto, no leaks!
I discovered in working on this that I'd forgotten to plug my low coolant sensor plug in ages ago. I last checked the coolant level about 70 miles before I noticed the pool of water on the floor, so here's hoping I haven't overheated something
