Sad really that people make a mockery of a system, nay institution, of how to write a letter.
Nowadays, l'm really surprised that people can actually string words together to form sentences correctly in their true grammatical form!
Dear Sirs - it's yours faithfully
Dear Mr/Mrs/Ms whoever, it's yours sincerely.
Depending upon the content of the letter itself, you would only add without prejudice, should you not want to have the contents of the letter thrown back at you in a legal situation. This is usually only for letters requiring settlements of a kind, but if unsure, inserting it would do no harm whatsover.
You have obviously sent your letter, so good luck!