Goalkeeper Eldrett first came to prominence shipping 15 goals for Baldock Town against Tufnell Park as an 18-year-old in the 1932/33 Amateur Cup. In 1935/36 he signed for Finchley and in the second half of the following season season he moved on to Enfield.

He signed for Wimbledon for the 1937/38 season and started the season as #1 but by December he was a regular in Crystal Palace's reserves and towards the end of the season he was back between the sticks at Enfield.

He was one of several ex-Dons players to end up at Sutton United in the 1938/39 season. One of his first matches was against Enfield and their forwards were described as "having as much chance of passing Eldrett as a baby whale has of shifting the Rock of Gibralter." As War broke out he had just signed for Barnet.