Yes, your passport will also serve as proof of living in the UK, specifically that you were physically present in the UK on the first day of your qualifying period, and that the stamps on the passport match the travel history you report in your application. Questions have arisen though, for those of us who have US passports and have been using the ePassport gate at the UK Border to get back into the country, because our passports don't get stamped when we cross the border.
If this applies to you, have a careful read of
Home Office guidance for its staff how to consider applications for naturalisation as a British citizen, specifically Page 16. My reading of this is that the stamped passport serves as the primary proof of living, but it can be backed up with correspondences you received at your address during the qualifying period (i.e. from them it would be common-sensical to conclude that you have been living here.)
In my case, I decided to put together a small collection of correspondences, 2~3 per each qualifying year, from HMRC, NHS, bank and local council. I then wrote a short note
Please note that, as a holder of a biometric passport of the United States of America, I have been able to use the e-Passport gate at the UK Border to enter the country since May 2019. Because of this, there are no UK entry passport stamps in my passport corresponding to the three foreign trips I took during the qualifying period listed in the application. The passport shows entry and exit stamps of the destination country for these trips. I have provided scans of select correspondences I received during the qualifying period as additional evidence for my residing in the UK.
and submitted the scans as supporting documents. Whether this helped or was just an overkill (perhaps Home Office does have electronic records of my coming and going that the case worker can access), I have no way of knowing. All I can say is that it apparently did not detract, since my application was approved and was in fact processed in very good time.
Does anyone else have any more clarity on this matter?