HE,HE,HE, you two. I've got that in my garden. No idea what it is, but it takes over the minute I turn my back. It's in my hot dry front garden, nr the house wall. Well, I think that's where it started, but now it's everywhere. It IS a beast! I've cut it, pulled it, dug it and accidentally (on purpose), poisoned it. Ha, it laughs in the face of my efforts I don't mind it, but not EVERYWHERE! in contrast, in the same bed is a lovely little pink Thrift like your white one in the centre. Oh, what a well behaved little critter gets only very sighlty bigger each yr, flowers loads, never needs trimmed or even dead headed. Unfortunately, she ends up getting a bit swamped later in the yr, but she doesn't seem to mind at all. Looks a little like a tiny wavy chive clump, very delicate.
I def agree with Dove (again!), sempervivens, house leeks, we call them, can be lovely. Really easy. Will increase quickly in the right place, but so easy to keep small. I shoved some in a crack in the front wall and jammed them in with soil, and they get bigger every yr and flower, making an ugly wall look quite pretty. There are loads of much prettier ones than mine, too, I had completely different ones in a wall where I used to live. You could do the whole sink in different ones. But keep the wee thrift!, She'll never let you down!