For students doing an exchange from Canada/US abroad, can you seek internship oppportunities in that country?

Hi all,
I'm preparing for the possibility of receiving an exchange offer, but don't want to miss out on relevant recruiting opportunities. I was wondering let's say if I'm a student from a target Canadian School and do an exchange in the UK for example, would I be able to work at a UK institution after my term? I say this from both a recruiting perspective, and also a regulatory perspective. Would I have to receive a special work permit to do an internship overseas, I want to do an exchange quite badly but if I do, it won't coincide with the recruiting timelines over here in Canada so I'm evaluating the option if possible of doing the exchange and internship across seas. If anyone has any ideas about this, please lmk thanks !