I'm Scottish (and live in Scotland). Traditionally, Scotch broth was made using cheap cuts of mutton, often on-the-bone. I make this soup regularly in winter. It's real winter comfort food!
However, you can use any meat you want, or none.
Meats I've personally tried include: cheap cuts of lamb, beef, chicken, even ham. Leftovers are also a good option. A left over roast chicken carcass is as good as anything. In my opinion it's best if the meat is on the bone. It adds something extra special. On occasion I've also used supermarket cartons of meat stock, or even stock cubes. The absence of one ingredient (meat) would never stop me from making one of my favourite soups!
I've also made it completely vegan before by using vegetable stock cubes as the base for the soup. The rest of the ingredients are already vegan, basically root vegetables, onions, leeks, pearl barley, peas, pulses etc. Whatever you have available really.
At its core, the broth itself is really just a vegetable soup. The uniqueness of the flavour (the thing that makes it "Scotch" broth IMHO) comes from the use of pearl barley which is used to thicken up the soup. Without the pearl barley, it would just be a vegetable broth. The other ingredients are variable/optional.