Tottenham Hotspur won the competition for the fourth time, beating Burnley 3–1 in the final at Wembley.
Matches were scheduled to be played at the stadium of the team named first on the date specified for each round, which was always a Saturday.
If scores were level after 90 minutes had been played, a replay would take place at the stadium of the second-named team later the same week.
Of the others, Ashington had last featured at this stage in 1952–53, Barry Town in 1951-52, Dartford in 1950-51, Grantham in 1949-50 and Banbury Spencer in 1947-48.
The final two non-league sides in the draw were Walthamstow Avenue and West Auckland Town, who were given byes to this round as the champions and runners-up from the previous season's FA Amateur Cup.
The 1962 FA Cup final took place on 5 May 1962 at Wembley Stadium and was won by Tottenham Hotspur over Burnley, by a 3–1 scoreline.