If someone has died without leaving a will, does the money go across (to a brother/sister) or go up to Father & Mother even if the deceased was not married/living with someone (and never had been) but had a small child (not living with them)?
As Ethel states, Scottish law is different to English law with regard to intestacy. However, in both England and Scotland, the child would inherit everything under the circumstances you describe.
As long as it's clear that the boy was the son of the deceased person, he's entitled to everything. That's true even if no father is named on his birth certificate or even if the wrong father is named on the certificate. As long as the deceased person was the natural father of the boy (and, of course, as long as no other children by the same or separate relationships exist), the child gets the lot.