The deed poll sites say you can use hyphens to link double-barrelled names, but the Home Office just says they will accept names with hyphens... They probably don't mean that "--------" is considered a valid name. But like, it'd be cool if it was.
As to why I didn't quote any laws, I can't find any. Name changes in the UK are largely "something people can just do", like changing pronouns, but a little more formalised. So it's probably not illegal to do that, just you probably want a name the Home Office won't ignore.