i am going through a discrimination tribunal myself atm, so will try to help where i can.
From the outset, it sounds that your employer has dismissed you because they believe that you took the sleeping pills, and the evidence of that is your behavior and their knowledge that you have suffered from a depressive illness before?
Have they stated this directly in any interview? Did they know of your previous illness and the reason behind your mistakes?
What was their explanation for the number of packs gone missing? Surely they cannot believe that you took them all?
It sounds unfair, because of their lack of evidence, and it sounds discriminatory because they have singled you out because of a previous illness.
The steps you HAVE to take next:
Appeal the dismissal.
Sucessfull or not raise a Grievance about how you have been treated.
If your Grievance is not upheld to your satisfaction, Appeal this decision.
If you wish to go to the Employment Tribunals, then you will have to fill out an ET1 and file it within 3 months of the dismissal/discriminatory event. This is very important if you wish to go to the Tribunal. It will take a long time for you to get wording right so if you feel strongly then start this now, but, when writing the ET1 you have to try to take all your emotion out of it, it is very hard.
There are lots of steps after this. The Tribunal route is stressful, very stressful and if you choose to represent yourself then it can lead to a lot of hard work and revisiting over and over again the injustice you feel has been done to you. Make sure you have a good set of people you can talk to, friends, relatives, doctors, therapists, all these people will help you.