Could this be the plant every botanist longs to be asked to identify? I remember the first time I came across it with Abbey's cousin David, a better botanist than I, and asked him what it was. He's a retiring sort of chap so I was somewhat taken aback by his seemingly abrupt answer.
I've not seen Mind-your-own-business in flower, but it does produce tiny flowers from May to August. Soleirolia soleirolii is a member of the nettle family but isn't native. It was introduced from the northern Mediterranean. Another common name for it is Corsican Curse: it was first described from Corsica and can easily reproduce vegetatively, making it something of a weed in some situations.