Yes, John Innes is a British thing, I remember it is what we used there even when I was just a kid going with my grandfather to get it at the allotment supplier. They would not call it (or Miracle Gro) compost here in North America either. Compost here is decomposed plant material. The Miracle Gro would probably be called "potting soil" here, even though it is soilless. John Innes does have an element of sand or mineral soil in it, although there are different levels (numbers).
"Recipes" for John Innes "compost" from the RHS:
https://www.rhs.org.uk/advice/...
