Few details of his life are certain. In 1510 he attempted to obtain the degree of BMus at Oxford University by submitting a mass and an antiphon; it is not certain if the degree was granted. Between 1510 and 1525 he may have lived in London, and may have had some association with the court of Henry VIII. Most likely he was chorus master at St. Mary Newarke Hospital and College in Leicester between 1525 and 1548. He was an applicant for the position of chorus master at Cardinal Wolsey's new Cardinal College, but Wolsey chose John Taverner instead. His exact date of death is not known, but he was buried on 17 November 1558 in Leicester, at St. Margaret's parish. Additional records show that a pension was paid to him up until that date.
Four sacred vocal compositions by Aston survive complete:
- Missa Te Deum (five voices)
- Missa Videte manus meas (six voices)
- Gaude mater matris Christe (five voices)
- Te Deum laudamus (five voices)
Other compositions survive in fragments.
In addition, he wrote keyboard music, most of which shows an unusually progressive use of idiomatic keyboard technique. Some famous pieces have been attributed to him on stylistic grounds, including the often-recorded and anthologized My Lady Careys Dompe. His Hornepype is also cited as an example of early idiomatic keyboard writing.