Typing an overdraft request letter to a bank isn't something that is done very often these days.
The best thing to do is to keep it brief and simple, state all the information they will need, such as:
Full name
Address
Account number
Sort code
Your date of birth
And any security questions they may ask you (usually questions you've selected and given the answer to on a specific date).
Then explain how much you need to extend your overdraft by, why you need to extended it all of a sudden, and what your financial situations is like now and for the foreseeable future.
If all that sounds like a lot of work, you're right!
Which is why most people just call the bank up onthe phone and make an application for an overdraft then.
They will run a credit check based on your publically available credit history, and will probably tell you whether you qualify or not pretty quickly!