"Does a father have the right to know where his child lives in the UK?
If a father has parental responsibility (explained above) he has the same rights to that of the mother, and has the right to know where their child is living. This, however, may change if it conflicts with the child’s best interests. For instance, an abusive father may lose their right to know where the child is living.
The courts expect parents to behave reasonably and communicate openly with each other about things like this, although of course this may not always be possible. If you are being denied information about where you child is living you can apply to the court for a specific issue order."
https://www.family-lawfirm.co.uk/blog/a-fathers-rights-to-see-his-children/