I read these books sometime in the late 60s/early 70s in paperback in Ireland, so probably UK published. Short books, not much more than a novella. I can remember reading 4 or 5 books in the series. I think one of the books was called "The Trouble with Trilobites" (but I can't find it on Google) and one took place in Wales. The titles were similar - The Trouble..., The Matter .. and may have been alliterative.
Unbenownst to all aliens have invaded and, disguised as humans, are plotting to take over. The hero (an American scientist or professional) discovers this by accident and, in the process, kills one or is involved in his dying. The body disintegrates as soon as the alien dies but the death is seen to occur and he is identified as the killer. He is then on the run (a) from the authorities who want to arrest him for murder and (b) the aliens who want to kill him because he knows they exist.
Each book takes place in a different part of the world. Following clues when he can, the hero travels around battling the aliens, all of whom (frustratingly) turn to dust when killed, so he can never prove anything. The plot is therefore a bit like The Fugitive (e.g. he meets a girl, but it cannot be). Don't know if he ever found a solution.