The earliest examples of an intentionally polygonal coin in what is now the UK are the Civil War siege pieces. Below is a diamond-shaped shilling struck by the Royalist defenders of the Nottinghamshire town of Newark in 1645/6 (picture from Tony Clayton's site). There was a ninepence and a half crown in the same 'series', IIRC.
Pontefract in the same situation issued octagonal coins (a shilling in this case):
I share coffeetime's admiration of the UK's heptagonal coins, and I like the 1982-2008 20p the best of our standard circulation coinage since 1971.
When it comes to tokens, there are many more variants to investigate. I have several similar to the one below; it's hard to determine how many sides it's got!
Triangular ones exist, too:
I'm sure I've also got one of a similar shape to the Brookbanks one but which is bimetallic, with the central part being an irregular shape (possibly a letter of the alphabet), but I can't find my record of it to plug it into Google for an image.