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If you have a rack you may just about manage but they're reasonably padded so don't fold that small.
I think you'll struggle to find anything that protects the bike, lets you pack in some luggage and you can also ride to/from the station.
There's this one which packs into a rucksack https://www.amazon.co.uk/RockBros-Travel-Folding-Bicycle-Transport/dp/B072X61N9B but not sure what you'd do with the rest of your luggage or how protective it is.
I have one of these https://www.vincita.co.th/collections/brompton-bags/products/b132b-soft-transport-bag-for-brompton-bike and tend to borrow one of these https://www.vincita.co.th/collections/brompton-bags/products/b206b-garment-bag-for-b132b (although I'll be buying one when I get round to it). They're OK although the airline did break it last time it was used (but accepted responsibility and replaced with a new bag). The bag comes easily in normal checked suitcase size for most airlines so doesn't need to go as sports goods/oversized, etc.
Stick the brompton in folded, a bit of bubble wrap on some of the protruding areas, use the garment bag filled with clothes to pad out the top and sides and there is also space to slide a couple of bags with clothes, etc down the sides. I normally go with a C bag down one side and a rucksack down the other.
SJS have the hard version of that bag available https://www.sjscycles.co.uk/transporting-bicycles/vincita-b132c-transport-box-for-brompton/