I've made 2 recommendations about baggage, the one above relates to the "personal item", where BA's size limit includes a 15cm width - very few bags meet this standard. The other bag I've suggested - though it doesn't really meet some of the OP's requirements is this Skypak. I use this as a sole bag for longer trips, 2 weeks and more, whereas the Aerolite above is OK as my only bag for a one nighter.
In between, there is a version of the Aerolite which is somewhat bigger, but conforms to easyJet's "one bag" requirements. This would last me 2 to 5 days as an only bag.
Because it's bigger than the personal item size for BA then it would have to count as your only bag, but it's nearly twice the capacity of the first linked Aerolite. All 3 bags are very tough, the Skypak has a well noted cloak of invisibility around it, you won't be asked to check it in.