His productions included Butley by Simon Gray, How the Other Half Loves by Alan Ayckbourn, Shakespeare's Twelfth Night, Blythe Spirit by Noël Coward.
His production of Class Enemy by Nigel Williams[7] won the Binkie Beaumont Award for Best New Director.
[citation needed] Alexander joined the RSC in 1977 as assistant to Trevor Nunn and John Barton.
In 1986, Alexander's production of The Merry Wives of Windsor won him the Laurence Olivier Award for Best Director.
[15] Alexander's other productions for the RSC included A Midsummer Nights Dream (1986) with Sean Bean as Robin Starveling, Twelfth Night with Harriet Walter as Viola, and Deborah Findlay as Olivia 1987/88,[16]The Merchant of Venice with Antony Sher as Shylock in 1987, Cymbeline with David Bradley and Harriet Walter in 1998,[17] Much Ado About Nothing in 1991,[18] The Taming of the Shrew in 1992,[19] and Titus Andronicus in 2003.