I'd urge you and strongly advice to contact them ASAP by webform.
https://secure.cic.gc.ca/enquiries-renseignements/canada-case-cas-eng.aspx. But you already did that
If I were you I'd explain the whole ordeal and ask them for two points:
1/Ask for extra time to do the biometrics
2/Ask for a letter in order to do the biometrics or a travel document you can use to do biometrics and to travel to Canada (it's a Blue passeport given to refugees).
May I ask a dumb/personal question but this may probably help with the issue? Do you have threats from your home country's government or some other threats not related to the figure of law? The reason why I ask this is because if you don't have issues with your government, you may go to the embassy and ask for another passeport?
Check also if you can apply for a refugee travel document in UK
https://www.gov.uk/apply-home-office-travel-document