For reference, the info is here:
https://www.canada.ca/en/immigration-refugees-citizenship/services/application/application-forms-guides/guide-5289-sponsor-your-spouse-common-law-partner-conjugal-partner-dependent-child-complete-guide.html
You'll have to scroll down.
A conjugal partner is:
- a person who is living outside Canada,
- in a conjugal relationship with the sponsor for at least one year, and
- could not live with the sponsor as a couple because of reasons beyond their control (e.g. immigration barrier, religious reasons or sexual orientation).
This term applies to both opposite and same-gender couples.
You can sponsor a
conjugal partner if:
- there is a significant degree of attachment between the two of you, implying not just a physical relationship but a mutually interdependent relationship, and
- you’ve been in a genuine (real) relationship for at least 12 months where marriage or cohabitation (living together) hasn’t been possible because of barriers such as sexual orientation, religious faith, etc.
Important: If you’re applying in the conjugal partner class, the person being sponsored
cannot be living in Canada.
I have bolded/underlined the parts I think most relevant. In simplest terms, they
usually treat these as dual requirements to be considered as conjugal - or if you prefer, requirement for dual barriers to becoming a marriage/common law couple is needed to qualify as conjugal.
1) Cannot get married because of some legal barrier (eg forbidden same sex, intrareligion, ban on divorce, etc); AND,
2) Cannot become common law (eg and usually because the putative applicant cannot get a visa to Canada (so as to establish common law).
And short form, as brits you could get married easily, or you could come to Canada and remain long enough to become common law.
You will therefore not qualify as conjugal.