Just as in the United States, an actor who is a non-citizen and does not have work permissions would need the proper visa to work in film, TV, and theatre within the United Kingdom. It is important to note that while the UK is a part of the EU (European Union), people who live in EU countries may work freely within the UK. EU countries are Austria, Belgium, Bulgaria, Croatia, Republic of Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, and Sweden. Further, EEA (European Economic Area) countries also enjoy the same work rights. EEA countries are Iceland, Liechtenstein and Norway. Switzerland does not belong to either the EU or EEA, but they too are able to work within the UK.
How to Obtain the Proper Visa
The United Kingdom government website will explain all of the information about what it takes to get the Tier 5 (Temporary Worker - Creative and Sporting) visa. It touches upon eligibility requirements, the documentation that you need to provide, the application process and the fees involved, how to extend or switch the visa, etc.