It's nothing to do with where you are "resident" and I agree the term can be difficult to define. All the passport renewal application (in the UK) requires is that you are "in the UK at the time you make the application". So yes, you can simply visit in order to get a new passport. The address you use doesn't have to be your permanent place of residence. Likewise, you could get your UK passport renewed in another country if you were simply abroad on holiday or business, without having to be a resident of that country.
The forms for either can be downloaded online and this makes it all a bit clearer.
A2QFI says: "I see you you don't live in UK - lucky you". Not sure if you mean me or the others, probably both. Thing is, there's no luck involved whatsoever - a concious decision made exactly for the reasons you mention and the many others one could rant about indefinately.