Frank Williams and Matilda Jackson met ten years ago. Three years later, Matilda moved into Frank's house, which he inherited from his parents. There is no mortgage on the property. After the couple had been living together for five years, they decided to try for a baby. Unfortunately Matilda did not get pregnant and so the couple decided to have fertility treatment. They attended all the appointments at the clinic together. Matilda was implanted with an embryo created using her egg and the sperm of a donor. Nine months later Matilda gave birth to a daughter, Betty Williams. Three months after the birth of Betty, Matilda and Frank separated because Frank was having an affair with a colleague, Amy. Matilda has asked Frank for money for herself and Betty, but Frank says that he is not required to pay her anything as they are not married. Frank earns £700 per week gross. Matilda has said that she will not allow Frank to see Betty if he does not pay her any money. She has also said that she plans to change Betty's surname to Jackson.
Discuss the legal position in this case.