Here's a selection of "complaining language" from the British Council, Madrid Adults. Particularly formal language is in italics.
Some introductory sentences:
I am writing to you to express my indignation/ outrage that
I feel I must complain about the manner in which
I am writing to you following a most regrettable incident
I am somewhat concerned about something which occurred
I am writing to you because I feel I can no longer put up with - direct!
I feel I must express my deep unease at the manner in which
I would just like to mention a little problem which has cropped up/ arisen concerning
Detailing the complaint:
I was absolutely outraged to learn that - direct!
I find it quite appalling/ most regrettable/ totally unacceptable that X should + verb - direct!
It is quite beyond belief that a grown adult should + verb - direct!
I was quite amazed to discover that - direct!
You can imagine my surprise when
It is rather unfortunate that he should + verb
Apportioning blame:
The whole thing was a cock-up (informal) of the first order - direct!
It is patently obvious that your company is to blame/ at fault in this matter - direct!
This was a gross discourtesy/ error on your part - direct!
Of course you yourself had no idea what was going on - direct!
Expressing your sense of personal injury:
This disagreeable incident has caused
I felt rather upset/ embarrassed about the whole thing
The whole thing has left rather a nasty taste in the mouth - direct!
Suggesting a solution:
I am sure you will agree that the whole business should never have happened in the first place
I feel that the least you can do now is to
I hope this business can be settled amicably
I sincerely hope a solution to this business can be found promptly
I look forward to receiving a prompt explanation as to what action you intend to take in this matter
I am sure that given good will on both sides a mutually-acceptable solution can be found
I would regret having to take this matter further
I would be most grateful if you could look into this matter and let me know what you intend to do about it
I believe I am entitled to a refund/ an apology.