This is copied from CHC London official website.
Responsible for Permanent Resident Applications from:
(Includes economic immigration and family sponsorship)
Channel Islands, Denmark, Falkland Islands, Faroe Islands, Finland, Greenland, Iceland, Ireland, Isle of Man, Norway, Sweden, Scotland, United Kingdom
Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, UAE, Yemen, for federal economic immigration only
Pakistan, for all economic immigration and family sponsorship applications
It clearly says they are responsible for economic and family immigration for Pakistan
Copy and paste this in your browser and see for urself
cic.gc.ca/english/information/offices/missions/london.asp