All businesses are required to have a registered office address in the UK under Section 86 of the Companies House Act 2006 also in Specific State in United States for LLC. You may not feel that you need an official office address if you run your business abroad or entirely online, but you still need a registered office in the UK.
Companies House and HMRC will send all official documents to your registered office address and assume that the company has received them at that address. Same thing during LLC. Other government bodies will also use your company address and are used for official communications and notices.