I'm rewatching White Rabbit. And I think I know what Jack did.
Judging from the way the conversation with his mother went, I think Jack probably told the medical board about his father's drinking problem. And as a result, his father lost his liscence to practise. That why his mom said his father had no friends. That's why Jack said he hadn't spoken to his father in two months and that it's likely his father didn't want to talk to him.
His father left for Austraila because he was pissed at losing his liscense and went on a binge that lead to his death.