FATHER SIMEONIt is my conjecture that they are twin brothers.
Brother Bernard joined an order which has dedicated itself to helping their fellow man find a cure for whatever their addictions may be. He has risen in the order to the point where he is in charge of a seminary-like clinic in London. It is there that he sought to help Brian Lane of UCOS to find his way back from his need for alchohol.
Father Simeon chose to follow a darker path. He immersed himself into the study of arcane lore in the hopes that he could defeat the half-lifes that plague Mankind.
Father Simeon liked for others, especially Luke Rutherford the so-called "last of the Van Helsings", to think that he was centuries old. Truth was, Father Simeon was a half-life himself. He had died a few years before* and was able to use the dark arts to keep himself "alive" in a zombie state. Whether or not his twin Brother Bernard knew about this, there's no evidence in that episode of 'New Tricks'. It wasn't relevant to the case at hand for UCOS.
*I don't think Father Simeon could have been "un-dead" for more than a decade. When Luke and Ruby found his body in the final episode of the series (having been "killed" by Gladiolus Thripp), there wasn't much evidence of corporeal corruption. Well, there were the flies that emanated from his mouth, but they could have been part of the spell that kept him "alive" and were now freed from their bondage.
I also believe that both men decided to join religious orders after the nearly tragic transformation of their father into some kind of creature with a gas mask for a face. This happened during World War II and can be seen in the 'Doctor Who' episode "The Empty Child". This would make their father Doctor Constantine, who must have been settled in middle-age when he fell in love and married, producing twin sons around 1936. The fact that their father survived such a transformation would have been deemed a miracle by the Constantine twins, who had no idea of the involvement of the Doctor. And so overcome were they by this miracle that it shaped their future lives. But they interpreted the event differently and so chose their paths accordingly. Brother Bernard Constantine sought to help other men overcome their problems, while Father Simeon Constantine strove to vanquish these bizarre creatures if it was already too late to save them from the transformation.
As for other characters played by Richard Wilson, I don't think Dr. Constantine was a "playuh". We should instead invoke the Toobworld principle of "Identical Cousins".
And with regards to Gaius, the mentor for young 'Merlin', he's in an alternate TV dimension and would play no part in the ancestry of all these other men. As always with my "Theories of Relateeveety", this is speculation.