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Under the Matrimonial Causes Act 1973 courts have jurisdiction over maintenance for 'children of the family.' A child of the family doesn't have to be a natural child or even adopted. The considerations are how long the family existed and what sort of responsibilities were undertaken. If the children were maintained during a longish relationship then perhaps it wouldn't be deemed unreasonable for financial support to continue.
However, my understanding is courts have no jurisdiction over child support when CM is claimed through the CSA. The children in their own right will be able to apply for financial support for uni from their natural father under schedule 1 of the Children Act 1989.