There are 4 UK Coenagrion species having females with solid black on the dorsal side of the abdomen.
First and foremost are the so-called dark/green forms of the widespread Azure Damselfly (Coenagrion puella) and the quite wide-ranging but patchily distributed Variable Damselfly (Coenagrion pulchellum). Happily these have quite distinctly shaped rear edges to their pronotums.
The remaining 2 species exhibit pronotums similarly shaped to each other. However, these 2 do not co-exist, one being the Northern Damselfly (Coenagrion hastulatum) restricted to Scotland and the other being the Southern Damselfly (Coenagrion mercuriale) limited to southern England, south Wales and Angelsey. Though similar to each other, these pronotums are also clearly different from those of the more widespread species.
The above image of a female Coenagrion mercuriale pronotum comes courtesy of Fturmo, CC BY-SA 4.0, via Wikimedia Commons. I have enlarged, rotated and annotated the original.