***** NOT A TEACHER *****
I would suggest something like this:
Dear Mr. Smith:
If possible, I would like to start my annual leave on 1 January.
1. Kindly remember the word is spelled "grammar."
2. In English, one always capitalizes the word "I."
3. One always capitalizes the names of the months.
4. In American English, one usually writes "January 1."
5. I was not 100% sure what you meant by "remaining annual leave," so I will leave that sentence to another member. I can tell you that it should be "in December or January."
6. Your sentence needed appropriate periods (full stops). You will see how important this is when another member corrects your complete note.
Student or Learner