Hello, I am Keith, one of the experts on Just Answer, and happy to help you with your question. I am a great believer in the written word in these matters so one has a hard copy record of what has been said or discussed. Spoken word is not recommended, there is far too much chance of the person at the other end getting hold of the wrong end of the stick, if they can even find the stick at all!
There are two letters to be written here.
The first is to HMRC to appeal against their tax calculation. This appeal is simply a letter pointing out the facts that actually you only had a few weeks health benefit and a copy of the letter from the health care provider will support your position. HMRC will, one hopes, correct their stance and reduce the amount of tax claimed. At this stage their actions have been perfectly proper as that Department is operating from the [incorrect] P11D.
You must also write to your old employer requesting them to resubmit a correct, revised P11D to HMRC.
That is the way forward. As far as you personally and your tax bill is concerned, the letter to HMRC should solve the problem. I do hope that I have assisted you with my answer and shown you a way forward.