Perilla frutescens? Def. not Persian Shield - (Strobilanthes dyerianus) which is tropical. It would help if these plants were labeled with botanical names. You want to make sure you're not getting something invasive!

I only had time to skim this...it's kind of counter-productive to entirely delete an original post no matter how annoying a response was. Another problem though with replicating the so-called English border style in the States is that, even if you can manage to grow the plants...they will be over in a flash and never all bloom together as you see them doing in pictures there. Our springs are too warm and sunny...too much like the UK summer. Then when our actual summers come, of course they are too hot for many of those plants to bloom well. I actually can't think of a really good example off the top of my head, although, for example, in a warm spring the wild foxgloves I used to allow to grow in a part of my garden seemed to completely finish blooming in less than two weeks. I suspect they can usually last much longer in the UK. And of course it depends on the plants, as well. Some people in the south would argue that they can substitute plants to give a similar effect, for example Lantanas can have a long bloom period. But of course those are different plants and have a different look to them. A handful of US gardens have replicated the style well - ones in better climates like Filoli's huge English border - and obviously there are some in the PNW too. The Cresson Garden in suburban Philadelphia pretty remarkably feels like a miniaturized English estate garden. Where summers are mild on the east coast like Martha's Vineyard I sometimes see pictures that look pretty darn close to English summer gardens, minus of course the lush broad leaved evergreens. Although some people fight that tendency like the Sakonnet Garden in coastal RI, which is pretty mild by northeastern standards and has some of the classic UK rhododendron cultivars like 'Aladdin'. This post was edited by davidrt28 on Wed, Nov 12, 14 at 16:44

You are free to disagree all you want but it doesn't change the facts. Lythrum salicaria is one of the top 10 invasive species in both this country and Canada. It is listed as an invasive species in 47 of the 48 contiguous states and in all the bordering Canadian provinces. It is also illegal to grow, sell or distribute the species and any garden cultivars of the species in 17 states. It is not that it 'could escape' or 'could pollinate' - it does, and that fact has been well established. They are all the same plant - it's just that selections were made for garden cultivation with the assumption that the seeds they produced were sterile. This has been determined to be false. Garden cultivars are just as likely to produce fertile seeds as their wild cousin and the seeds will not necessarily come true to form. In other words, they can revert. And that fact is behind the prohibition of any named cultivars in states that restrict or prohibit sales. One of the issues that always seems to stir up discontent about the validity of invasive species is that it is often not obvious in a garden setting that they are invasive so the assumption is made they are not. This is a fallacious assumption. Each plant of Lythrum can produce as much as 2.7 million tiny seeds which are easily dispersed by wind and water. They can travel great distances, land on moist soil, overwinter and then germinate. As they prefer moist/wet conditions, infestations disrupt wetlands and waterways and alter ecological conditions, overwhelming native plantings and altering habitat and food sources for wildlife. Forget-me-nots and orange daylilies are not considered invasive because they do not cause ecological or economic harm, which is a major factor in the definition of an invasive species and is the criteria purple loosestrife meets with open arms. Annual control costs, loss of habitat and disruption of agricultural crops run into the millions of dollars. Vinca and English ivy are considered invasive in some areas and certain regulations apply to them as well. There are so any other great garden plants that pose no threat to the environment that it just doesn't make sense nor is it very responsible to persist in growing what is one of the most significantly invasive plant species we have to deal with.

Leucanthemum vulgaris, the meadow ox eye daisy type, would have a basal rosette, and they don't grow rhizomes (IME). Symphyotrichum (aka Asters), would be my bet too, I planted/ handled some several times, this foliage reminds me of S ageratoides, only problem there are several species, sub-species and cultivars, so really tricky to be sure which it is, plus I have no clue whether they could prosper without winter dormancy, good luck, Lin