I carry a full size spare but you need to pack up the boot floor by around 50mm to clear it.
I use 50mm builder foam/isulation.
when i bought the polysurround i believe the jack was then included along with the wheel clamp/securing bolt.
I retain the jack and poly surround from my 2013 car, the jack is definatly not provided with my 2015 car. But oddly the lever bar, part of the jack handle was.