Would you be able to hear a badger running away? I've just been in the garden and I've disturbed something, low to the ground, got a general impression of where it was but you could hear it thud as it ran over the patio bit. If it was a fat cat it couldn't have run that fast.
Could well be badgers in my opinion, I've seen them run across the road at night and they tend to bob up and down, as they run like other members of the weasel family.
A muntjac would have alarm barked, badger would be my favourite . Don't feed it unless you want your garden wrecked you aren't allowed to disturb them if they set up home