Red-Legged Black Spider

I wish this wee spider had properly introduced itself before shinning down on a thread and disappearing, but I was too busily occupied to give chase*.
It's quite tiny, about 7mm - that's tile grout it's sitting on - but I'm sure it has a proper name that, someone, somewhere out in Blipland, might know.
Do tell, in case it appears again and we can address each other on first-name terms.
*Actually it hadn't travelled far so it's currently in a jar, swearing blue murder.