If you watch a few BBC shows, you quickly realise that the pool of actors is relatively small (compared to US productions) and there isn't the same TV vs. movie actor stigma.
J.K. Rowling also didn't want her characters to have American accents (or Americans doing crappy British accents) so all of the significant actors are British/Scottish/Welsch/etc.
The crossover is most likely that both productions are looking for the same types of actors off a fairly short list. If you drop out actors who aren't "USA-friendly" (bad teeth, older, heavy accents) you get an even smaller group.