Most companies in the UK are private limited companies (LTDs). They are legally distinct entities with their own assets, profits and liabilities. The personal finances of any shareholders are protected by limited liability (ie their liabilities are limited to the value of their shares). Shares in private companies cannot be offered to the general public.
Private companies must be incorporated with Companies House (Companies House in Edinburgh for companies registered in Scotland, and Companies House in Wales for companies registered in England and Wales) and are required to adopt certain legal documents - including articles of association and a memorandum of association - which form the company’s constitution.
Limited companies must have at least one director (who must be a natural person, ie a human and not a company) and optionally a secretary. The directors will often be the sole or primary shareholders. They have various legal duties, one of which is to ensure that an annual return is submitted to Companies House every year.
For more information, read Private limited companies.