Not registered keeper but insured to drive my friend car, can I tax it with my documents?

Did you receive the road tax reminder (V11) to renew the tax disc? If you have the V11 form, you can get a new tax disc provided you've got valid insurance on the vehicle and proper MOT as well. If you haven't got the V11 form, you can still renew the tax disc with the registration certificate (V5) at the post office. It might be worth getting a letter from the registered keeper if you're going to a Post Office branch though.

If you do not have the required documents to tax the vehicle, the cashiers at the post office will refuse to supply a new tax disc.  If you know all the details about the vehicle and it's got valid insurance and mot, it might be easier to do it online.