Before talking about this question, we should learn about the definition of sheepskin at first. Here is the explanation from Wikipedia: Sheepskin is the hide of a sheep, sometimes also called lambskin. Unlike common leather, sheepskin is tanned with the fleece intact, as in a pelt. And for sheepskin jackets and coats, are clothes made by sheepskin!
Which is known to all that mainland of Europe are temperate maritime climate, one in which there aren't extremely hot or extremely cold temperatures. And one of the finest weather on earth, so that human beings and animals live in this place are all pleasant and comfortable! But for UK and Ireland, separated from Europe land and influenced by ocean more than land, cause extremely cold temperature in winter. And the sheep (lamb) are all around England, so when stepping into winter, sheepskin became the most common used material for clothes. And this is why some sheepskin coats and jackets and pretty popular in UK!
Actually sheepskin is used to produce sheepskin leather products and soft wool-lined clothing or coverings all over the world. And in Oceania, sheepskin is the main material for produce footwear, because Oceania is also the place of origin best quality sheepskin.
In UK, there are so many different styles coats and jackets nowadays, all designed by latest fashion designers. And those designers create some new types of funky coats like: soft shell shearling coats, sheepskin leather jackets, sheepskin long coats, and the most popular style can be the vintage sheepskin coats. A classical country needs some never out of fashion style clothes!