When I posted my old passport off (after applying for a new one online) two months ago, the Passport Agency site was showing a waiting time of around 5 weeks and that did indeed turn out to be how long it took for my new passport to arrive.
Mrs NJ and I did ours online and they both took eight days to arrive. Did them on a Monday, arrived a week on Tuesday. This was four weeks ago. Our old passports took a little longer to be returned.
I really recommend applying online if you can. We had our photos taken at a photographers. He provided us with a code which you enter when making your application and it links to your photograph. No uploading, nothing. Piece of cake!
Further to NJ's post, many (but not all) photo booths issue a code to enter on your passport application form (rather than needing to upload anything). The one I used in Morrison's did, giving me a strip of four photos, with the code printed above them. It accepted card payments too, so I didn't need to find change for the machine.