A functional definition of a British naval yard is more useful here than a narrow formal rating. Most substantial British yards can perform at least some naval work, although specialist yacht yards are an exception. Falmouth counts because it services Royal Fleet Auxiliary ships and conducts Royal Navy offshore-patrol-vessel maintenance and refits. That definition complicates direct comparisons with Canada, where the questioner describes yards through a more explicit naval-rating system.
Notable Point · 49:42-50:20
What counts as a British naval yard
A British yard can count as naval through maintenance and refit work even when it also serves civilian shipping.