Peters played only five games in his first season with West Ham. Although he played 32 league games in the 1963–64 season, he played no part in their FA Cup run and was not selected for the FA Cup final of 1964 at Wembley, in which they beat Preston North End 3–2. The following year, however, he established himself as a first team regular and was victorious at Wembley when West Ham won the European Cup Winners Cup with victory over 1860 Munich. He was usually partnered in midfield by Eddie Bovington and Ronnie Boyce.