Travel Question

I need to get from Melbourne to Ithaca in late July, and it seems (oddly) that the cheapest way to do this will be to fly to London on one airline, change planes and then fly to Ithaca (or at least Syracuse) on another airline. This should lead to an interesting exchange with the immigration people.

bq. “Why are you in England?”
“To change planes, I’ll be out in a few hours.”
“Where did you fly in from?”
“Er, Bangkok.”
“And are you delivering drugs to anyone while you’re here?”
“Er, why do you ask that? I mean, if I was a drug runner, I’d try to have an itinerary that looked a little less like a stereotyped drug runner wouldn’t I? Wouldn’t I?”

So I was wondering whether anyone’s done something like this before and whether the immigration people get upset if you use their country as a transit lounge?