Earlier this year my wife and I decided to renew our passports with about six months remaining on them.
We went to a Crown Post Office (Bristol in our case) having previously ascertained that no appointment was necessary. The counter clerk took our photographs and entered our details digitally on application forms. She then took possession of our old passports to return to the Passport Office. At the time the Press was warning that passport applications could take several months and the counter clerk told us it could take up to eleven weeks.
This was on a Wednesday. On return home the same day email acknowledgements of receipt of the digital applications awaited us (we don't have smart phones, only a desk top computer). On Thursday further emails told us the applications were being processed and on Friday I was told my new passport was on its way. It was delivered on Saturday just three days after I had applied for it. My wife's new passport arrived two days later on Monday. Our old passports were returned to us about a week later.
It cost a few quid more to go via the Post Office route but we considered it well worth the extra money.