Does moving in with family if you are lonely at home alone (e.g. single person or student without their own family except parents and siblings) count as leisure travel, or essential travel depending on your purpose?

I actually know of someone leaving the US and moving to Sweden until this blows over as 'they have distant relatives' over there. I also know of some Italians going back and forth to their families with those daily Alitalia flights. Areas with large affluent 'foreigners' such as South Kensington and Knightsbridge feel really empty even allowing for lockdown, it seems most of the people with family abroad have left.

I was also talking in the context of June as per the thread, which by then many measures would have changed, so if leisure flights are permitted without quarantine, I would assume the bigger airlines would have bigger coverage (e.g. BA still has flights compared to Easyjet who do not fly at all)