He was one of Britain’s greatest military leaders but letters coming up for auction in the new year reveal a less noble side to Admiral Lord Nelson: petulant, jealous and complaining.

Two of the letters are from Nelson to his lover Emma Hamilton, another is written by Hamilton and a fourth features the couple writing together. They shed fascinating light on Nelson, his palpable and obvious love for Hamilton, and how he was probably more at ease when he was fighting.

“I’m afraid it is often the case that Nelson is not at his best when he is inactive,” said Gabriel Heaton, a books and manuscripts specialist at Sotheby’s, which will sell the letters. “In the final letter you can just sense the frustration, he can complain quite a lot … he is itching to get back to what he knows he does best.”

Nelson’s affair with Hamilton was one of the biggest public scandals of the time. They met in 1793 when he was a 35-year-old married captain and she was 28, the wife of Sir William Hamilton, a diplomat.

The Nelson-Hamilton letters being auctioned by Sotheby’s. Photograph: PR

The couple were head over heels in love and Heaton said that came across in the letters. “They had a very deep love for each other, the depth of affection between them is so obvious when you read their correspondence. They are not Victorians, they are not afraid to express their emotions.”

Nelson could also be extremely jealous and one letter in the sale reveals his anger with the Prince of Wales, who seems to have been flirting with Hamilton.

“I … am sorry that you cannot go to a Public place without being tormented by that fellow who has not the smallest regard for sir William [Hamilton’s husband], I hate and detest all the Great and I would not associate with such Company for the World.”

At the time of writing, Nelson was anchored in the Thames estuary waiting, impatiently, for the conclusion of the Peace of Amiens talks. He goes on to promise that he will return to her as soon as he can, that he will “not stay one hour after hostilitys [sic] cease”.

A portrait of Lady Emma Hamilton. Photograph: Culture Club/Getty Images

It was a time when small things really mattered and in another letter, to his brother-in-law George Matcham, Nelson expresses his contempt at the behaviour of his wife, Fanny, who seems to have visited the Matchams and left a card without seeing them, even though Mrs Matcham was at home.

“He writes with cold fury about the behaviour of his wife,” said Heaton. “This is very much the world Jane Austen is writing about and while Nelson does not often come across as a character in a Jane Austen novel, you do have moments here where it is very much that world.”

To modern eyes Fanny’s behaviour seems trivial. “In the complex social hierarchies and appropriate behaviours of the time this was a very marked gesture of impoliteness,” said Heaton. “He was furious at his wife at her impudence, as he sees it, towards his sister and brother-in-law.”

Nelson hands the writing over to Hamilton in the same letter and her style is very different. “She has a wonderful, very gushing way of writing,” said Heaton. “She is always wildly enthusiastic and excited or hopelessly, hopelessly upset.”

Heaton called it “a very nice and interesting group of letters … There is a lot of detail here which really sheds light on Nelson and Emma and their immediate family and puts them in the context of the French wars.”

He said there was a strong market for such first-hand accounts of the lives of significant figures. “There are many people out there who treasure history and would want to have a fragment of history.”

The letters will feature in a sale on 17 January that also includes what the auction house calls “an exceptionally large” fragment of the union flag from HMS Victory. Measuring 86cm by 92cm (34in by 36in), it is part of the flag believed to have been flown during the Battle of Trafalgar and has an estimate of £80,000-£100,000.