I don’t know about UK. In Germany, unmarried fathers are systematically discriminated against. Custody, alimony and financial support from the state are setup all with the mindset that the mother takes care of the children and the father makes financial support. There’s no equal rights there, this is the assumed default. Deviations have to be explained again and again for taxes, child allowance, retirement subsidies and and and. In cases of doubt the money goes to the mother, and there is no arbitration other than going to the courts.
The other thing that comes to mind is the dealing of the police with domestic violence. Whenever anyone calls the police for domestic violence, the police automatically assumes the man is the offender. Even if the man was the caller, it’s he who is taken into custody. This is systematic discrimination.