Mike, we had lemon balm in our garden in Northampton.......over a couple of years it spread like wildfire, it was absolutely everywhere.  We seemed to be forever pulling up tons of it.  I've never grown it since!

Yes Lemon balm once planted takes on a life of its own- we have it popping up everywhere. I would not recommend planting soapwort either- it spreads by runners and is like couch grass in that if you leave a piece of root in the ground it grows away again.

God, bloody feverfew, in my early gardening years here, I bought a golden feverfew, I'm still pulling up blooming plants every summer.

A friend of mine when I said I think my borage plant has died said "you can't kill borage" which at the time I thought was strange, but he was right, it self seeds everywhere.