Hey Claire -
This spring I travelled from Michigan (US) to the UK with a very hard-to-replace Taylor Limited Edition guitar.
I queried a number of folks and the consensus was DO NOT try to take it on board, as the airport folks have a vast discretionary powers as to what gets on board and what does not. You might be in transit - and prevented from taking it into the cabin. Then you might be faced with having to check or gate-check it without adequate protection. Gate-check is risky without a true travel case. These are expensive!
My friend Abe, who takes his guitars all over the world, places them in an extra thick gig bag, thence into a big cardboard box with styrofoam peanuts or bubble wrap. You check it and just unpack it at the other end. It may go thru as "oversize baggage" but for a musical instrument there may not be an extra fee (check with your airline).
I needed to travel by Tube and rail once in the UK so I got a travel case from CaseXtreme. I put my "baby" in a Taylor gig bag, thence into the CaseXtreme case, and had absolutely no issues, no problems there and back again.
For multiple instruments, I would do some variation of the above, unless you could reliably arrange for good instruments to be loaned to you at your destination.
Good luck on your gig!
Rutger