Without claiming the two systems have the same limiting factors, the UK health system is also struggling, and there the staff shortage is the government's limits on (1) how many spots universities have, (2) immigration.

This is despite health in general, and the HNS in particular, being a major source of interest for the electorate.

Alternatively (or also) pay scales and emigration. There are doctors leaving for Australia (which advertised golden handshakes & Australian lifestyle in the UK to UK doctors) and nurses for better pay/conditions in private care facilities; it's not (just) a supply of trained people at source issue.

Salaries are also much more compressed than in North America - UK junior doctors generally earn more than NA residents, but then not that much more (maybe 4-5x from lowest to highest, not >10x to reach hundreds of thousands) as consultants (attendings). Locum pay & additional private work can make up for some of that, but probably not all, and I assume similar could be done in NA if you wanted to earn more (or open their own practice, pharma sponsorship, etc.)

It's probably true in general (relatively compressed salary ranges) actually, not just in medicine.

A large fraction of the new doctors in my town in Canada are Britons who have emigrated here. The Canadian government is actively recruiting them.

Why could that be? Does that factor into your assertion?

What the Canadian government does isn't as important as the (now previous) UK government telling foreign doctors to keep away while also not offering enough local people the opportunity to train to make up the difference between supply and demand.

The UK government has no power to keep people in (though my own departure shows they could do a better job of not making people want to leave in the first place), but it does have power over the other two.