I once heard a myth which went along the lines that somewhere in the North of England there was a sheep (or other animal) which, if approached at the correct time (probably midnight) and date, would speak the day of your death (I'm not sure exactly how it went though). Unfortunately when I've tried to find out about this my searches have drawn a blank. Does anyone know of a myth like this, or did I just imagine it?
It is very likely that you didn't imagine it: in the folklore of the British Isles beings of different shapes (often shape-shifting) who foretell one's death are extremely common. What you describe seems like a variation (perhaps very local?) of various legendary creatures attested in Northern England. Here are few examples which are somewhat reminiscent of your description:
- Padfoot (from "The Encyclopedia of Celtic Mythology and Folklore" by Patricia Monaghan):
In Yorkshire, this strange donkey-sized creature appeared as an omen of death; it looked like an amorphous shaggy ball with eyes or a wooly white dog.
- Barguest (from "A Dictionary of English Folklore" by Jacqueline Simpson and Steve Roud):
This is the name for a particularly alarming shape-changing bogey animal in the folklore of Yorkshire, Lancashire, and other northern areas, which might be encountered at stiles and in dark lanes, or near churchyards. Sometimes it was only heard, not seen; it howled and shrieked, and to hear it was an omen of someone’s approaching death—possibly one’s own.
- Guytrash (from "A Dictionary of English Folklore" by Jacqueline Simpson and Steve Roud):
A frightening shapechanging apparition, usually in animal form, in the folklore of northern England. [...] (It) appears mostly as ‘a black dog dragging a chain, a dusky calf, nay, even a rolling stone’ [...] a North-of-England spirit, called a Gytrash, which, in the form of horse, mule or large dog, haunted solitary ways [...] Another possible form is that of a large cow; to see it is an omen of death, for oneself or another.
- Shotton Dobby (from "A Dictionary of English Folklore" by Jacqueline Simpson and Steve Roud):
In County Durham, the Shotton Dobby appeared at births or deaths in the village, as a goose, dog, horse, donkey, or cow.
Unfortunately, none of these completely matches your description, but it should give you an idea of how abundant such folk motifs are in Northern England, and how likely it is that the myth you heard belongs to this category.