[2] In 1977, Eve joined the cast of Franco Zeffirelli's Filumena,[2] in London's West End, where he met future wife, Sharon Maughan.

[7] In television, he appeared in A Sense of Guilt in 1989, and the 1992 BBC production of A Doll's House with Juliet Stevenson,[1] whom he also worked alongside in the BAFTA and International Emmy Award-winning political drama The Politician's Wife.

[1] Eve won the 1997 Laurence Olivier Award for Best Actor in a Supporting Role for his portrayal of Dr Astrov in Uncle Vanya.

[8] He then went on to star in the 1998 Carlton Television/WGBH Boston television series Heat of the Sun,[1] which was filmed in Zimbabwe, and portrayed the titular character's wicked stepfather Edward Murdstone in BBC's 1999 adaptation of David Copperfield opposite Daniel Radcliffe and Maggie Smith.

[1] In 2010, Eve played the father of the female lead, his real-life daughter, Alice, in She's Out of My League,[1] and starred as Peter Manson in the ITV/Mammoth Screen remake of Bouquet of Barbed Wire.

[1] In January 2011, he starred in the three-part ITV drama Kidnap and Ransom,[1] filmed on location in South Africa, and reprised his role as Dominic King in 2012 for the second series.

[1] Eve played the part of Judge Sir Selwyn Hardcastle in the BBC's Death Comes to Pemberley in December 2013,[1] and as Roach in The Interceptor in 2014.

[1] On 19 February 2014, Eve was part of the invited audience at Buckingham Palace to celebrate the centennial of the Royal Academy of Dramatic Art.

He and his wife were asked to perform in front of the Queen in the Investiture Room, along with Hugh Laurie, Sir Tom Courtenay and Dame Helen Mirren.