The emerald damselfly (Lestes sponsa) is not uncommon in Britain but it does tend to favour shallow water and is very tollerant of acidic bog pools so it is on the damper areas of Dorset heathland that you will most frequently encounter them. They are also quite able to survive in sites that dry out in late summer as it over winters as an egg rather than a larvae.
I think there is some confusion over identity of this species. The banded agrion and beautiful demoiselle are both a lovely emerald green and some assume that this means they are the emerald damselfly but this only goes to emphasise the difficulty of our English names which can be quite misleading at times. There is an additional problem with this speciess too. With a distinctive bright band around the tail the emerald damselfly can easily be dismissed as a blue-tailed damselfly as the emerald green colouring really shows up best in good light. However, the best distinguishing feature is that the emerald rests with its wings at 45 degrees to its body rather than along its back. Add this to its preferred choice of habitat, heathland, and it becomes quite simple.
The emerald damselfly can be seen from May right through until October but are most common in August and September.