Teacheranne
Pepper might be your cheapest option, together with a sign for the owner.
There was a lump of poo on my back lawn today and I assumed it was a fox but my decorator said it was from a badger! I’ve seen foxes at night but not badgers so I must keep an eye out.
My front garden is open plan and we are not allowed to put up fences but I’ve planted prickly hedges all along my boundaries which seems to deter people and dogs wandering over the lawn - but was not cheap!
Fox sounds more likely.
All the badger poo that I see around us (and we are surrounded by badgers) tends to be in shallow, open holes. It's very rural here though, so I suppose it is possible that they might have different habits in less rural areas.
I think you would soon know if badgers regularly visited your garden - they can quickly do a lot of damage with their scratching in search of food!
But they say that getting a man to wee around the perimeter will deter them. It might deter your neighbours too, though