I don’t think firms are harsher as such, especially now there is not any form of residents labour test that needs to be done for people not transferring from a student visa (which used the be the case pre January 2021).
I do think firms look closely at motivations for international candidates though and often have an additional layer of why commercial law in the U.K. rather than another country that a lot of domestic students don’t have to prove in the same way. Firms know the English training system is one of the quicker ones in the world and that it makes many people more employable in other jurisdictions. They don’t want to train people for them to leave upon or shortly after qualification, especially in jurisdictions where they don’t operate.