I think the narrowness of the channel makes it difficult - with shared responsibility in parts. Australia are pretty much in the middle of nowhere which might make it easier (I'm guessing there though).
Yep, it's a legal minefield. Plus if the Navy were deployed, it would take significant resources - i.e. rescue equipment, medical attention, food, etc. Plus you have to get these people assessed/processed. There would also likely be some casualties at some point and that wouldn't look great for the UK.
It's a difficult one. As easy (albeit callous) as it sounds to stick some warships out there and point guns at people until they turn around, it's not really viable.