Calling a Damselfly the ‘Azure Damselfly’ makes it sound much more exotic than if you called it the Blue Damselfly. There are, however, multiple UK Damselflies which are blue, so Azure it is; Coenagrion puella.
Apparently the male has a characteristic flat-bottomed “U” shaped mark on segment 2. Who knew? The females of the different damselfly species are a lot more difficult to tell apart. Unless, that is, if one of them is being dragged around by the neck by an enthusiastic male partner. Then we can, I hope, safely assume he has correctly identified the correct species of female.
Here are a pair in tandem:
Their bodies make a slightly squashed love-heart shape together.