Just reading about the siege of El-Arish in December 1799. Seems a Lieutenant Colonel John Bromley was present with John Douglas of the Marines, both serving with the Turkish troops. I am not sure about the identity of John Bromley.

The life of Sir Sidney Smith says he is a French emigrant:

"He ... afterwards embarked with Sir Sidney Smith, in the Tigre, and entered the Turkish service, at that time, as Colonel Bromley, where he aided, by his able advice and assistance, the grand Vizier. At the peace of Amiens he returned to France, and got rank in the French army. He was even in the battle of Waterloo, in the French service, and in command of a brigade."

Seems a bit far-fetched?