Janjal is 100% correct. The British embassy etc. cannot advise on anything outside of their jurisdiction.
The role of an embassy is not to sort out problems for their own citizens. The main role is to support and promote their own country's business and political interests.
The consulate may be able to help you if you get into trouble, but often they can't. It is a minor role and they have no jurisdiction here either.
I often look at the Canadian embassy in Beijing site to see what they say about travelling or living in China.
The information they post about visiting or living here does not match my experience here at all.
I think it's all made up by some person in Canada who has never been here.
The same may be true for other foreign embassies.
So WHERE can we get accurate information about renewing/extending visas beyond the end of the automatic two month extension?
Visa info is always the Entry and Exit Bureau. See article for phone number and call them.
"information they post about visiting or living here does not match my experience here at all"
Ditto that. Then again they must build their view on the cities and places where majority of the repsective nationals visit, and those are Shanghai etc.
Scams on West Nanjing Road and petty thefts in places are (or have been - haven't been to such in years) a real thing, but nothing that describes life in Kunming for example.