Kemp is definitely an Anglican priest; he has a wife and children, and in the 'church sequence' he wears the style of surplice common in the church of England; with a green stole (indicating it took place in 'ordinary time - i.e not in Lent/Advent/Christmas/Easterdide or some other festival).
If I were writing the scene, I'd have had Kemp actually celebrating the Eucharist (Mass, Holy Communion - different words for the same sacrament), rather than simply reading the narrative of the last supper.
I am an Anglican priest (happily one whose ministry is to date untroubled by vampires, LOL), and what I can tell you is that some parishes and priests are indistinguishable from Roman Catholic ones, and that many Anglicans will refer to themselves as 'Catholic' - but not 'Roman Catholic'. And of course, it is not impossible in Kemp's back-story that he was ordained as an RC priest, but later switched to the Anglican Church, and subsequently married; there are plenty of examples of this, as well as Anglican clergy converting to Rome.
It's funny as a clergyman, I do pick up on little things like the vestments, etc, and how, sometimes, TV and film companies get it wrong. Sometimes very much so, but its only a few churchgeeks like me who notice.
Being Human did get it right; if the service was a Communion, then Kemp is dressed in a way that many Anglican priests would; Cassock, Surplice, and Stole in the appropriate liturgical colour for the season. Most of us, and especially in the more Anglo-Catholic end, wear the same Eucharistic vestments as RC clergy - alb, stole, and chasuble, but the way in which Kemp is dressed, assuming the service is a Eucharist, would indicate that his churchmanship was 'middle of the road', rather than full-on Anglo Catholic. Of course, he is correctly vested of Evensong & Sermon, and I think that this is what the service is, in the episode.
Anyway, just wanted to comment, and I am so enjoying the series; a wonderful way to chill, after Sunday services and duties are finished.