Dfyjkt

My background: UK citizen, Canadian Permanent Resident.

I applied for Global Entry via the UK Government website but upon proceeding with the application I was told I am ineligible as a landed immigrant of Canada 1 (Canada cannot be selected from the radio buttons) and that I should apply for the NEXUS program instead.

When reading the requirements for the NEXUS program, I read that I need to be resident in Canada for three years before applying. Since I've only been in Canada for 19 months I do not qualify.

Is a British citizen in this situation eligible for any of the "fast track" entry programs?

Got my rejection letter from the CBA today and the check box ticked was because I failed to meet the residency requirements of the program.

The minimum is 3 years despite the ambiguity of the website.

I think you can apply for NEXUS, though the requirements are ambiguous.

Prior to 2012 all NEXUS applicants, regardless of citizenship, had to be resident in Canada or the USA for the prior 3 years. In 2012 the residence requirement was eliminated entirely for Canada and US citizens, and the 3 year requirement was done away with for "certain permanent residents".

Unfortunately I can find no authoritative reference for who is a "certain permanent resident", but I believe the 3 year requirement was in fact eliminated for everyone and replaced with simpler requirement that the permanent resident actually live in the country where they have residence (for a Canadian PR in particular it is possible to live outside Canada for an extended period without losing the status; for a US PR not so much). I believe this because I know the 2012 changes were meant to align NEXUS qualifications with US Global Entry qualifications, and GE has no 3 year requirement.

In any case, lacking more authoritative information, it might be worth just applying for NEXUS to see if you are a "certain permanent resident" since you can't lose much beyond the $50 application fee by doing so. I suspect you'll need to provide documentation showing that you actually reside in Canada, but the fact that you've lived there for less than 3 years won't be a bar. As a Canadian resident you have no choice but NEXUS in any case, so it is that or nothing.

The 3 year residency is residency in either US or Canada as a citizen, permanent resident, or resident alien of these two countries check this link

Depending on which website you check, the requirements can be stated ambiguously, e.g. some non-CBP and non-CBSA/GC websites states you have to be a resident of the country you are a permanent resident in, for 3 years. Other websites state differently. I think you should be a resident of either of these two countries for 3 years, even if you are not a PR in the country you are living in, but PR in the other country. E.g. my application was approved since I am a Canadian PR but living in US for over 7 years.

No. I am not sure why I can't submit just "no": you are told you are not eligible for Global Entry, and you were told correctly, so says the CBP:

Canadian citizens and residents are eligible for Global Entry benefits through membership in the NEXUS program.

and you can clearly see you are not yet NEXUS eligible. How could we help? What did you expect?