IJWTF as a current EZY employee I sympathise completely. I would question whether the so-called "Crew Helpdesk" has ever been monitored or fit for it's stated purpose. As for anyone reading a letter.....
If you need a letter for reference purposes as in your dates of employment with a company it would be quicker to contact the Inland Revenue Helpline. They will issue confirmation of your five year history within a couple of weeks in my experience.
The last phone number I used was 0845 302 1458 when I needed assistance.
Hope this helps