The American speedwell (Veronica peregrina) arrived in Britain before 1680 but was originally confined to gardens. It isn’t the world’s prettiest plant so probably arrived by accident with something much more garden worthy. It’s favourite habitat is flowerbeds in gardens and parks or cultivated ground such as allotments.
The plant has an upright habit similar to British water speedwells. It could easily be mistaken for a willowherb since it has similar-shaped, non-hairy, opposite leaves and grows in the same kinds of disturbed ground that many of the small willowherbs favour. But the fruit is a short, broad, two-lobed capsule typical of speedwells rather than the long pod of a willowherb.
There is a large population of plants on the cultivated experimental plots behind the greenhouses near the Harborne Building. Or there was on the 23rd April. Weed-killer is regularly sprayed around the plots to maintain an earth boundary and I left it too late to take a photo.
There are some good pictures available by Patrizia Ferrari.