Martyn was transferred to Crystal Palace for a fee of £1 million in 1989, becoming the first goalkeeper to attract a million-pound transfer fee in English football. He remained at Palace for seven seasons, appearing 349 times for his club, including the 1990 FA Cup Final (where Palace were beaten by Manchester United in a replay), and the 1991 Zenith Data Systems Cup final (where Palace beat Everton). In 1996, he signed with Leeds United, setting another record fee for a goalkeeper of £2.25m.