Looks like Veronica longifolia.

Agree, it does look like Veronica of some sort.

Thanks for that & they could well be, only in the web pages I've looked at say it flowers from July onwards - not in May!

I'd like to get a couple of these plants for our balcony!

There are a few cultivars which start blooming in May such as Incana. This one looks like Veronica 'Purpleicious' which does begin blooming in May.

Thanks very much, you may well be right, Bathgate. I've looked up both the names suggested & there seems to be very little difference between the two.

It doesn't really matter which it is to me as I'm not actually growing it myself, though I would like to. It's growing in the flowerbed the council plants up every year & I was intrigued to discover its name as I pride myself on being able to identify 100s of plants without having to think about them very much.