I agree that the branded buffs are rather overpriced (although I've not seen them as high as £20), but as has been noted you can get them very cheap from places like Amazon. I use them instead of a hat, because I kept on losing hats which are quite expensive. Since I've reached the point in life where my natural head covering is moving off somewhere, it helps to be able to cover said parts when the sun shines as it has recently. I tend to use it as a headband to stop the sweat getting into my eyes, and then as the sort of pirate hat when I need the aforementioned protection. At the end of the walk I remove it and wrap it around my wrist so I don't put it down while having a pint and then go leaving it behind (as happened to hats). In fact wrapped around your wrist can be useful for wiping your brow if it's really hot.
In winter I tend to use it as a scarf, and again, when I get to the pub or similar I just wrap it around my wrist so again, I don't forget it. If the weather is particularly inclement, it can again be used as a headband, but covering my ears, and also as a cowboy bandit type mask if it's really cold.
Just one thing, the cheap ones do tend to be tighter than the branded ones, and probably don't use material of the same quality, but if you can wait you often see the branded items reduced in outdoor shops.