STEP 2 - Starting your letter: focus on the facts
A good letter of complaint is written in such a way that it can be put before a judge at a later stage of the dispute. Stick to the bare facts, [2.1.] remove all expressions of emotion, and look at the events from a distance, as if they happened to someone else, a stranger.
If you find it helpful, think of your letter as the Captain’s log from Star Trek. What was the date of your flight? What was the flight’s number and destination? What was your ticket number? What went wrong?
Focus on what facts are needed to demonstrate your legal right for what you are seeking. For example, if you were bumped, state that you had a confirmed reservation, that you had all necessary travel documents, and that you presented yourself on time for check-in and boarding, but you were nevertheless denied transportation.
Do not talk about how you are a long-time loyal customer and do not raise moral arguments. [2.2.] The employee reading your letter does not care that you were upset.
The above's authors don't have law degrees. The above is for Canada, but Canadian Contract Law has adopted much of English Contract Law; so some relevant precedents: Jarvis v Swans Tours Ltd  EWCA 8, Farley v Skinner  UKHL 49,
I agree with everything above except 2.2 (that should be distinguished from 2.1). Mustn't you communicate emotional or mental discomfort or distress or suffering from the difficulty somewhere in your letter, if you're seeking compensation or damages for distress or disappointment?