An explanation is necessary for this list. The BDS list of UK species seems ambiguous in that it includes pure migrants whilst I want a list of UK resident species.
I began with the 44 species of Odonata taken from Britain’s Dragonflies (Smallshire and Swash). These were the so-called “breeding species”. However, that included Sympetrum flaveolum (Yellow-winged Darter), with which I disagree; S. flaveolum has, in the past, invaded our shores on a few occasions and apparently has bred but at teh time of editing  it hasn’t been seen for more than 20 years – it certainly ain’t resident IMHO.
Conversely, over recent years we have consistently seen a few newcomers in the UK. Both Lestes barbarus (Migrant Spreadwing/Southern Emerald Damselfly) and Aeshna affinis (Blue-eyed Hawker/Southern Migrant Hawker) are regularly seen in Kent and/or southern Essex. Originally regarded as migrants, they are now seen at consistent locations which I’d say indicated breeding colonies rather than yearly migrations, which would be unlikely to end up in exactly the same spots every year. Coenagrion scitulum (Dainty Damselfly), having once been a resident species that was thought to have been wiped out, was rediscovered in 2010 and is now apparently surviving on the Isle of Sheppey and a small part of Kent. So, these I have included in my resident list. The list also includes Anax parthenope (Lesser Emperor) as a yearly visitor rather than as a breeding resident. Thus I have ended up with my UK list of 45 species.
Species which are linked to a species page, I have seen (though not necessarily in the UK). Unlinked entries, I am yet to see. As a result of a successful though weather-plagued trip to Scotland in 2017, I am now down to one species remaining to be seen.
- Calopteryx splendens (Banded Demoiselle)
- Calopteryx virgo (Beautiful Demoiselle)
- Chalcolestes viridis (Willow Emerald Damselfly)
- Lestes sponsa (Emerald Damselfly)
- Lestes dryas (Scarce Emerald Damselfly)
- Lestes barbarus (Southern Emerald Damselfly)
- Ischnura elegans (Blue-tailed Damselfly)
- Ischnura pumilio (Scarce Blue-tailed Damselfly)
- Enallagma cyathigerum (Common Blue Damselfly)
- Coenagrion pulchellum (Variable Damselfly)
- Coenagrion puella (Azure Damselfly)
- Coenagrion mercuriale (Southern Damselfly)
- Coenagrion scitulum (Dainty Damselfly)
- Coenagrion hastulatum (Northern Damselfly) 
- Coenagrion lunulatum (Irish Damselfly) 
- Erythromma najas (Red-eyed Damselfly)
- Erythromma viridulum (Small Red-eyed Damselfly)
- Pyrrhosoma nymphula (Large Red Damselfly)
- Ceriagrion tenellum (Small Red Damselfly)
- Platycnemis pennipes (White-legged Damselfly)
- Aeshna mixta (Migrant Hawker)
- Aeshna affinis (Southern Migrant Hawker)
- Aeshna isoceles (Norfolk Hawker)
- Aeshna grandis (Brown Hawker)
- Aeshna caerulea (Azure Hawker) 
- Aeshna cyanea (Southern Hawker)
- Aeshna juncea (Common Hawker)
- Anax imperator (Emperor Dragonfly)
- Anax parthenope (Lesser Emperor Dragonfly) 
- Brachytron pratense (Hairy Dragonfly)
- Gomphus vulgatissimus (Club-tailed Dragonfly)
- Cordulegaster boltonii (Golden-ringed Dragonfly)
- Cordulia aenea (Downy Emerald)
- Somatochlora metallica (Brilliant Emerald)
- Somatochlora arctica (Northern Emerald) 
- Libellula quadrimaculata (Four-spotted Chaser)
- Libellula depressa (Broad-bodied Chaser)
- Libellula fulva (Scarce Chaser)
- Orthetrum cancellatum (Black-tailed Skimmer)
- Orthetrum coerulescens (Keeled Skimmer)
- Leucorrhinia dubia (White-faced Darter)
- Sympetrum danae (Black Darter)
- Sympetrum sanguineum (Ruddy Darter)
- Sympetrum striolatum (Common Darter)
- Sympetrum fonscolombii (Red-veined Darter) 
 – Limited to Scotland.
 – Limited to Ireland.
 – Not a breeding resident but has been recorded every year since 1998.
 – May or may not be resident but if not, it seems to re-colonize and breed every year (it can manage 2 generations a season).