Scilla siberica, Siberian Squill and Puschkinia libanotica, Striped Squill.

Sue it's a form of Euphorbia. It's a tiny cultivar of Euphorbia leucocephala http://www.burkesbackyard.com.au/fact-sheets/in-the-garden/flowering-plants-shrubs/euphorbia-leucocephala/#.VLoKL9KUddw and I think it's known in the trade as "Diamond Frost " or similar They can sucker, and they will die down over winter, when you can cut those canes right back and hopefully your plant will re-shoot in spring. Euphorbias like those have a white, latex-like sap which is an irritant so be careful handling it and keep kids and animals away if poss. Here is a link that might be useful: link

Hmm, Knotweed - I think you're right. Thanks.

Even 'full' sun is pretty weak here at this time of year and I wouldn't worry too much about acclimatisation. I also believe that the PM would clear up outside because it prefers dry conditions, low light and poor air circulation. Especially if you trim off some of the worst affected stems. I am wondering whether you got these plants from the veg section of a supermarket rather than a garden centre? If so they are grown fast and sappy for consumption in the kitchen rather than more robustly for planting in the garden and they don't usually last long.