It is hard to pick one director as the biggest British director, as the film industry is filled with many talented and accomplished individuals. However, some notable and accomplished British directors include:
Sir Alfred Hitchcock
Sir David Lean
Sir Richard Attenborough
Christopher Nolan
Danny Boyle
Stephen Frears
Mike Leigh
Ken Loach
Steve McQueen
Sam Mendes
This is a subjective list and there are many other notable and accomplished British directors throughout the history.