dulciusexasperis and MoreMilesPlease are indeed correct! I was originally thinking something along the lines of what is commonly found in US supermarkets, although more specifically something like what is found in blood banks -- thick walled, straight sided, with a well-fitting lid (as linked by MoreMilesPlease). After reviewing the options that you have all kindly provided, I think we will probably just opt for a soft-sided cooler bag type situation, packed safely away inside a cardboard box. My goal is to bring some goodies home from the UK, which I'm hoping won't be a problem on an 8 hour flight in March.

Thanks again for all the suggestions!