Hard One: Anyone know this movie?

Ok so I don’t know any of the actors, or the director, or even if it was a Hollywood film (I have a suspicion it may have been British in fact). But the plot might ring a bell if anyone’s seen it:

There has been some sort of nuclear disaster and the whole planet is destroyed except for 5 or 6 men, 2 women and a cat, that get marooned on a desert island. They can hear nothing on the radio, and assume everyone else is dead. The men (including a priest) take it upon them to restart the human race, by impregnating the younger of the two women (the other one is too old). And in the rest of the film they fight each other off for mating rights, until they all eventually kill each other.

I saw this one on BBC around 1995, and I think it was fairly new at the time, so I’m guessing late 80s, early 90s…does it ring any bells?