$25 was with Virgin Atlantic. From my impression a very good airline all around, but I've only flown with them on that one trip yet. They charge $25 as a standard fee for any outsized/overweight bag regardless of what you put in it.

I don't know what the name/brand of the case was unfortunately. Just whatever the bike store was renting out. Very large which was cumbersome on crowded London trains, but easy for packing the bike.