I am not sure what you mean when you say you 'pay your expenses back.' You're not an MP are you?
If you mean you only claim for expenses that you incur for business, your employer may well be right in putting them on your P11D, and that you should put in a claim to HMRC to prevent being taxed on them. As you say, this seems like unnecessary bureaucracy. Most employers avoid this by obtaining a P11D dispensation. This saves them the bother of putting the expenses on the P11D in the first place. But they have to apply for the dispensation - it's not automatic.
AK