I believe you should have been charged £7.50 excess fare to upgrade your off-peak fare to an Anytime fare, providing the date on your ticket was for the day you travelled.
There was no need to pay a 'fine', just the difference in price between the peak ticket and the off-peak one. However your poor communication skills let you down I guess, saying 'I am happy to pay a fine' was a big mistake, and this probably resulted in the course of action we are seeing here.
If you had been an articulate businessman in a suit and had approached the ticket checker saying 'I have an off-peak day return could you please excess it to an Anytime Return', there would have been no problem.
Provided the ticket was for the day you actually travelled, this is a relatively simple matter and a letter along the lines of
To Whom It May Concern,
I am in receipt of your letter regarding my travel on [date] from Liverpool Street to Stansted Airport, and I would like to respond to the issues raised.
I had purchased an off-peak day return for [date] the previous night, because I believed my travel would be after 9:30am. However due to unforeseen circumstances at my work (I work a night shift), my travel on the morning of [date] was during the morning peak, at 7:45am. When I arrived at Stansted Airport I offered to the inspector to pay any 'fine' due for travelling on an off-peak ticket during peak hours. This I now realise to have been unfortunate use of language made because I speak English as a second language, and I now understand that the correct term is 'excess fare', under the National Rail Conditions of Carriage section 12.
I did my best to communicate my willingness to pay the excess fare, however the Inspector did not ask me to pay it and instead took my name and address and now I have received this letter.
I would like to repeat my offer to pay the excess fare, in accordance with the National Rail Conditions of Carriage section 12. The difference between the Off-Peak Day Return fare which I purchased, costing £24, and the Anytime Return fare, which is £31.50. Accordingly I have enclosed a cheque for £7.50 in settlement of this matter.
Yours truly,
Amit