Absolutely nothing (to paraphrase Frankie Goes to Hollywood).
Well, no that isn’t necessarily true. Exhaustive research (i.e. reading the Wikipedia entry about laurel) shows that it is actually where bay leaves come from (I didn’t know that), as well as being a source of essential oils used in aromatherapy and soap making, not to mention a chemical compound which supposedly inhibits melanoma.
All well and good, but that’s Laurus Nobilis. What we call laurel in the UK is actually Prunus Laurocerasus, which isn’t quite so useful. Possibly a pharmacological use, and floristry, but if you eat it you’ll be ill, due to it containing cyanide compounds (so well worth checking which variety you have before you chuck one of the leaves into your bolognaise sauce).
So, what my garden is overflowing with is the mostly useless, invasive, British variety. I can verify that it’s invasive, as it’s everywhere, and massive. It’s moderately attractive I suppose, but I also have a nicer mottled one (Aucuba japonica), and I can see that it’s pretty from a specimen six feet tall -the other fifteen feet is overkill.
The upshot of this is that the laurel in my garden is doomed. A few branches of the one over the shed have already succumbed to the chainsaw, and much of the rest will follow in due course. At least we’ll end up with some firewood (which burns with a brilliant flame, according to the Green Living Forum’s firewood guide), so I guess it does have some use after all.