Which of the following is a UK-based ballet company?

The Royal Ballet is indeed a UK-based ballet company, established in 1931 and based at the Royal Opera House in Covent Garden, London. It is known for its classical ballet performances as well as contemporary works. The company has a rich history and has played a pivotal role in the development of ballet in the UK, showcasing both British and international choreographers and dancers.

In contrast, the other options listed are not based in the UK. The National Ballet of Canada operates out of Canada, the Paris Opera Ballet is a prestigious company located in France, and the New York City Ballet is based in the United States. Each of these companies has its own unique contributions to the world of ballet, but they are all situated outside of the UK.