[1] He was educated at Salisbury Cathedral School and Wadham College, Oxford, and was called to the Bar from Lincoln's Inn.

[1] He presided as Lord High Steward of Ireland at the trial of Lord Santry for the murder of Laughlin Murphy in 1739; the verdict was guilty and Wyndham had the distinction of being the only Irish judge to sentence an Irish peer to death for murder (although Santry was ultimately pardoned).

His conduct of the trial, as was to be expected of a judge with his reputation for integrity, was exemplary, although the prosecution case was so strong that the outcome cannot have been seriously in doubt.

Elrington Ball praises him warmly as "a great gentleman", and one of the most distinguished members of an eminent family.

His devotion to duty, which may have contributed to the collapse of his health, is shown by his willingness to hear urgent cases at home, even during the legal vacation.