An overseas company must register with Companies House if they want to set up a place of business in the UK. This would mean that the overseas company has some sort of physical presence in the UK through which it carries on business.
If an overseas company does not have a physical presence in the UK, then they are not usually required to register with Companies House. For example, an independent agent who conducts business on behalf of an overseas company is not seen as the overseas company having a physical presence in the UK, neither is an occasional location such as a hotel where a director of an overseas company may conduct business during periodic visits to the UK.
If the overseas company is required to register, then they must submit a completed OS IN01 form and pay the standard registration fee of £20 to Companies House. If the company is registering its first UK establishment, it must also send Companies House a certified copy of the company’s constitutional documents and a copy of the company’s latest set of accounts (with a certified translation in English if prepared in another language).
The overseas company can be registered using its corporate name (its name under the law of the country of incorporation), or an alternative name under which it proposes to carry-on business in the UK.