TD, bit hard to post the laws without the facts, the house thing is a totally different ball game then the kids maintenance.
Birth cert names, his or hers, register with the UK or not, passports etc.
This may apply, or may not.
Section 1541. An action for repudiation of a child cannot be entered by the husband or the prior husband if it appears that the latter allows the birth of the child entered in the Birth Register as his legitimate child or arranges or agrees to have it entered in the Birth Register.
Or this may apply.
Section 1555. An action for legitimation may be entered only in the following cases:
Where a rape occurred, or an abduction or illegal confinement of the mother during the time when conception could have occurred;
Where elopement or seduction of the mother occurred during the period when conception could have occurred;
Where there is a document emanating from the father and acknowledging the child as his own
If in the Birth Register it appears that the child is a son or daughter of the man who notified of the birth, or such notification was made with consent of the man;
Where open cohabitation of the mother and father has occurred during the period when conception could have occurred
Where the father had sexual intercourse with the mother during the period when conception could have occurred, and there exist grounds to believe that he or she is not the child of another man;
Where there has existed a continuous common repute of being a legitimate child.