What does Companies House actually do?
It holds the public record of every company in the UK: its name, registered office, directors, shareholders and filed accounts. Anyone can look up any company for free, which is why suppliers, lenders and customers do exactly that before doing business with you.
Registering a company there is what creates it as a legal person, separate from you. From that point the company has obligations of its own, and Companies House is where most of the non-tax ones are met.
It is not HMRC. Companies House deals with the company's existence and public filings; HMRC deals with its tax. A new company is told about both, but the two are separate bodies with separate deadlines and separate penalties.