Your first stop should be with your bank as you have built a relationship with them and they can see that you pay in your salary. You should also feel safer about applying for the loan.
You will probably have to take some identification, and you may need to take the offer letter for your job (or contract) showing your employment details.
You can look at the money tab on this site and look at entering your information in but as you don't have 3 years of address history, and no other forms of credit this is more difficult.
Do you have a mobile phone contract? These are a credit agreement.
You need to make sure that you are registered on the electoral roll at your addresses as these need to be on your credit record.
Good luck
Sparky.