It's rare that such a common phrase can be pinpointed to a precise moment in time, and a precise man.
It happened at the Battle of Copenhagen. The British were commanded by Admiral Sir Hyde Parker and under him, Vice Admiral Lord Nelson. Nelson had an unfortunate tendency to lose spare body parts. By the time of Copenhagen he was missing an arm and an eye. The missing eye proved to be a decisive advantage in the battle.
Parker and Nelson had split their forces for a two pronged attack: Nelson to attack the Danes directly and Parker to block Swedish support. The wind turned against Parker, but took Nelson into the waiting Danes. The Danes, commanded by the Crown Prince, put up a furious and highly creditable fight. The cannon fire at close range between ships of the line was intense and deadly.
Parker could only listen to the battle and, fearing that Nelson was having the worse of it, raised the signal on his flagship for Nelson to disengage. Parker explained his reason thus: "If he [Nelson] is in a condition to continue the action successfully, he will disregard it; if he is not, it will be an excuse for his retreat and no blame can be imputed to him."
Parker was a fine man, but an indecisive leader. He had abdicated all responsibility as commanding officer present, and what more, if Nelson continued the battle in the face of the order to disengage and subsequently lost, then it would be Nelson's fault.
When the disengage order was pointed out to him, Nelson ordered the acknowledgement flag be flown, but also ordered to remain in place his own signal flag to engage the enemy closely. Thus Nelson took full responsibility for the continued attack.
By the terms of warfare at that time, it was a capital offence for a subordinate to flagrantly disregard a direct order. But in the fog of war -- and it really was a fog in those days with all the cannon smoke -- it was relatively common for a signal order to be missed.
The only problem was, Nelson's flag captain had seen Admiral Parker's signal and pointed it out to his boss.
Nelson solved the problem with these words:
‘You know, Foley, I have only one eye. I have a right to be blind sometimes’. He then put his telescope to his blind eye, and said ‘I really do not see the Signal!’
And so for the first time in history, someone had turned a blind eye to something he didn't like.
Turn a blind eye appears in literature only after the Battle of Copenhagen, so Nelson was almost certainly the source.
It raises a problem for the humble historical writer. Is it reasonable for a character to use the phrase prior to 1801?
The conceit is that we are reading in modern, everyday English, what was spoken 2,500 years ago in modern, everyday Attic Greek. I think of it as like "translating" an ancient text. To turn a blind eye references a well known event in 1801, no one in Classical Athens would have used it, and therefore it's not acceptable ancient usage.