The Royal Family has strenuously denied there was any cheating

Sarah Forsyth, 30, said the allegations contained in a letter was "like putting a gun to the headmaster's head".

But she denies her job loss was due to the standard of her teaching and claims unfair dismissal at a tribunal.

In the letter dated 25 June 2003, a �10,000 payment from the school was described as "derisory".

Ms Forsyth told the hearing at Reading, Berkshire, the comments were not made simply to "obtain a few grand from the school" but she did consider the amount "insulting".

"This wasn't a demand for money; I didn't demand money from the school but I didn't think that their offer of �10,000 was the way I wanted it dealt with."

Eton headmaster Anthony Little has said she was offered an ex-gratia payment, but denied it was any kind of pay-off.

Secret recording

The school has also denied the allegations in Ms Forsyth's letter.

She wrote that she had been asked by Ian Burke, her head of department, to help the prince by writing a text which was used in his AS-Level coursework journal.

Ms Forsyth said she had not spoken about the prince's coursework to anyone at the school during the year between the alleged incident and her sacking.

The letter was written to help her own position and to let the headmaster know about Mr Burke, she added.

She has claimed that parts of a painting featured in newspapers as the prince's A-level work were completed by another teacher.

And she alleged to have secretly recorded Harry thanking her for the help when it became clear she would not get her job back.

Teaching criticism

Eton has previously said Ms Forsyth's tape is inaudible in parts and, in any event, the whole issue is irrelevant to the dismissal.

Ms Forsyth made her claims in a letter to Eton's headmaster

The school maintains that three separate teachers saw her sitting with Harry working on his coursework journal.

The Royal Family have also issued a statement denying the Prince cheated.

In a statement to the tribunal, Mr Burke criticised Ms Forsyth's style of teaching, saying there had been complaints from pupils about her manner.

He said: "Subject matter was often puerile such as comic books, downloaded internet imagery, images from the National Geographic and photographs left by John Booth [the former head of department].

"There was often a dark and sinister side to the imagery, dwelling on death, horror and blood.

"For example, a boy who was suffering from cancer and whose mother had died was asked by Sarah to try and visualise the small cancerous growths within his body."

The court heard a tape secretly made by Ms Forsyth in which Mr Burke tells her: "I don't care about you as an individual. I care about the people who you're teaching."

The tribunal continues on Wednesday.