I think I may have found the answer to the Puzzle. I Tweeted (how appropriate!) about this and had a reply from @MarkAvery Director of Conservation at the RSPB who also has a blog Here Mark very kindly took the time to reply to me personally by email, which is very much appreciated and it here it is:
This is a strange story. But birds are aggressive creatures at times. They do have fights between members of the same species. And they do occasionally kill each other. Usually fights end up with one bird giving in and fleeing. Usually fights are in spring and summer when males of many species (including blackbirds) are defending territories.
December is rather early for blackbirds to be defending territories for nesting but nesting seasons are getting earlier and earlier so it is possible that it is to do with that. The male blackbird may have been defending a particularly good spot for feeding though.
I wonder whether the female was injured, perhaps by the cat or perhaps more unusually by the scuffle with the male blackbird, and because she couldn't escape she seemed, to the male, to be persisting in threatening his food supplies or territory. By not fleeing, the female was inadvertently sending the signal that she was continuing to threaten the male. So he kept on attacking. That's the best I can do! Not sure if that fits the facts well or not.
Well the only aspect that I find unusual is that a male would do this to a female - I would expect this kind of behaviour between 2 males. However, this happened during that extremely cold weather we had (in the UK) and if food was in short supply maybe the male was prepared to fight to the death.
So trying to fit in what Mark said with what I saw, the most likely explanation is that the cat injured the Female Blackbird. Because she was injured she couldn't fly off - the male took this as territorial behaviour, and a threat to his food supply, he probably tried to chase her off and it appeared she was refusing to leave and perhaps was challenging him. I am sure if she could have flown off she would have. [This would explain the first bit I saw where they were flying around each other.] So when she wouldn't leave he decided to attack her, and in her weakened state it didn't take much to kill her. Thanks again to Mark Avery for taking the time to explain this and solve the puzzle.
So to finish, a picture of a Male Blackbird - not the protagonist in the above story! But a picture taken in Ireland at my parents house.