The Financial Conduct Authority (FCA) is the UK's regulator of financial services businesses. It does not regulate banks or insurance companies with regard to their stability and soundness, which is the responsibility of the Prudential Regulation Authority which is part of the Bank of England. The Financial Ombudsman Service investigates complaints made by consumers (individuals, and small businesses and organisations).
Financial services businesses, and individuals in certain roles within them, most be authorised by the FCA. This ranges from laying down requirements to ensure firms are financially sound, to requiring that people in particular roles (notably those involved in providing advice to consumers) have at least minimal qualifications for their role.
It maintains a register of authorised firms, which allows the public to check whether firms are properly authorised or not (hopefully!) before dealing with them.