After the agent went off to check, apparently this is permitted, but I am likely to have the same restrictions (if not worse) very soon. I went to the chat this morning for clarification about whether or not I would be allowed to ask them to close my account, then create a new one. They do have the usual section saying that duplicate accounts may have their winnings taken at their discretion. Of course, this is all to do with gambling addiction. Something that took my interest was a section stating that we can ask them to close our accounts then if we create a new one, they hold no responsibility.
So after having my account at William Hill limited yesterday, I decided to read through their rules in regards to multiple accounts.