There are many famous modern British dramatists, and teir plays focus on a wide variety of different themes. the Angry Young Men focus on class conflicts, while Pinero wrote drawing room comedy and Beckett absurdist drama. Stoppard's works are highly intellectual and concerned with the nature of drama as a genre.
Themes are probably still similar to Shakespeare--family relationships, greed, incest, ambition, etc. Check out the following links for more info: