The letter should be short and simple: Just start Dear [name] and continue something like this:
I would like to request a transfer to X College with effect from [date] Please let me know if there are any questions about this.
Then add any information relevant to your situation and give a polite ending such as: Many thanks for your help.
I would like to request a transfer to X College with effect from [date] Please let me know if there are any questions about this.
Then add any information relevant to your situation and give a polite ending such as: Many thanks for your help.