Red dead nettle, Lamium purpureum.
This pretty plant is one of my two worst weeds. The other is twitch/couch grass, Elytrigia repens. Both limit what I can do in my garden.
The red dead nettle probably came with plants from a friend's garden. With careful nurturing little clumps will grow among her flowers. Here at a lower altitude and lower rainfall it flourishes without any help at all. It seems to be indestructible. It has a thick wad of fibrous roots which makes it difficult to pull or dig out. Pulling them out doesn't kill the plant, which will go on flowering as usual. There is no point in putting them on the compost heap. Digging them in is not effective either. They eventually push their way to the surface. This particular plant was, as a seedling, dug in deep and covered with 30cm of cut grass last autumn. Weed killer causes the foliage to turn shades of yellow and purple, but it will still flower.
Because of red dead nettle I can no longer grow carrots. The seedlings come up first and quickly establish a dense network of fine roots. Pulling them out also pulls out the carrot seedlings. I've tried snipping them off, but they are rapidly replaced. I have sown the carrot seed in trenches filled with fine compost, but the carrots don't do well. Most other vegetables I can start in pots or trays, but I do miss my carrots.