Yes, but the only possible way to obtain legal parentage would be by means of an adoption order. To apply for a parental order, it is a requirement to be married or in a civil relationship. Check the requirements for adopting a child in the UK above.
Read the full article on: How Does Surrogacy Work in the UK? – Law, Cost & FAQs ( 48).

Sara Salgado
Embryologist
Degree in Biochemistry and Molecular Biology from the University of the Basque Country (UPV/EHU). Master's Degree in Human Assisted Reproduction from the Complutense University of Madrid (UCM). Certificate of University Expert in Genetic Diagnosis Techniques from the University of Valencia (UV).