In theory, almost any Embassy/consulate with an immigration section can issue the visas/copr (eg in London). It comes up often enough for eg Indian nationals who happen to be in Australia or other places. And when I say 'in theory' I mean that definitely it can be done to submit passports in different countries entirely - if the visa office in embassy has the visa printer and the right blanks, they can do it.
Unfortunately tracking down how to do this and getting instructions is not always easy. If you have an email for Ankara immigration section, you could try them; or the high commission in London; or call IRCC in Canada; or webform. (Webform would most likely be the absolute slowest).
The other potential thing is to contact VFS in the UK to see if they can accept - there's perhaps a slightly better chance that VFS in UK will have run into this situation more often (and hence know that they can accept passports with the PPR even if the PPR did not come from London visa office). Or VFS chatline.
As always, the real issue is finding someone to speak to who can actually understand the issue and give clear instructions.
I assume your family is nationality of one of the countries typically covered out of Ankara (like Iran) but living in the UK (and have been througout the application process)? It really is a bit dense of Ankara that they didn't provide instructions that explain how to do this.
