Hi, and welcome to the forum.
Where was your child born, and what passport does he hold ?
It would make it very much easier for your child if you got him his own British passport before he travels anywhere.
The child's natural father still has rights as well as responsibilities for the child, and I think you should make an effort to find him and inform him of your intentions (unless he has previously been abusive or violent towards you or your child).
After all, although we have no reason to doubt your story, it IS your side of it only.