It should first be noted that there is no requirement for overseas companies to register in the UK if they do not have a physical presence (eg office or branch) - but they can do so as long as they provide a physical UK address. Furthermore, partnerships, LLPs, unincorporated bodies and government agencies cannot register as a limited company in the UK.
Overseas companies must register with Companies House (or Companies House in Edinburgh for companies registered in Scotland) within one month of opening a UK establishment. They can do so by filing Form OS IN01 'Registration of an overseas company opening a UK establishment' with Companies House - along with a £20 registration fee. If it is registering its first UK establishment, it must additionally provide:
- certified copy of company's constitution documents (including a certified English translation if required)
- latest set of company accounts (including a certified English translation if required) if it is required to file these in its own country
For further information on registering an overseas company in the UK, see Companies House.