When the child is born, the people who are to be the child's parents apply under s 54 of the Human Fertilisation and Embryology Act 2008 for a "parental order", which transfers the child's legal parentage from the woman who carried the child during pregnancy (and who is automatically "the mother" in law when the child is born) to the intended parents.
That's all quite progressive, in many ways, but there is an oddity. Section 54 says this:
“54 Parental orders
(1) On an application made by two people (“the applicants”), the court may make an order providing for a child to be treated in law as the child of the applicants if—
(a) the child has been carried by a woman who is not one of the applicants, as a result of the placing in her of an embryo or sperm and eggs or her artificial insemination,
(b) the gametes of at least one of the applicants were used to bring about the creation of the embryo, and
(c) the conditions in subsections (2) to (8) are satisfied.
(2) The applicants must be—
(a) husband and wife,
(b) civil partners of each other, or
(c) two persons who are living as partners in an enduring family relationship and are not within prohibited degrees of relationship in relation to each other.”
The question is why parental orders are available only on an application by "two people". (Insofar as two people apply together, I have no difficulty in the further requirements set out by subsection (2).) Two analogous areas of family law reveal that the law is, in general, accepting of single people becoming parents via state-sanctioned means, namely adoption and children born following assisted reproduction.
In terms of adoption, section 51 of the Adoption and Children Act 2002 allows an adoption order to be made "on the application of one person". Similarly, a single woman can receive treatment at a clinic and have a child using donor sperm, and that child will have only one legal parent.
Consequently, the law provides that:
-- a single woman may become a child's sole legal parent using donor sperm;
-- a single person, whether a man or a woman, may become a child's sole legal parent under adoption law; and
-- any "two people" who are a couple (whether married, civil partners, or in a stable cohabiting relationship) can become a child's legal parents via a parental order following a surrogacy arrangement.
Given these provisions, it is difficult to see any reasonable justification for preventing a single person becoming a child’s sole legal parent using a parental order. It cannot be said now (as perhaps it couple have been before the 2002 and 2008 Acts) that the law’s aim is that children have two legal parents, since there are two distinct ways in which the law allows a child to have a sole legal parent. Nor can it be said that the law has any policy of favouring, say, women as sole parents, since a single man can adopt under the 2002 Act (and in any case, such a policy would obviously be entirely unjustifiably discriminatory).
So what could be the aim? It is difficult to think of one. What we see here, I suspect, is a position reached by piecemeal development which has accidentally created an anomaly. However, this anomaly is unjustifiable and creates discrimination against single people -- especially single men, who have fewer ways of becoming a parent in the absence of a partner than do single women.
It's a small point, perhaps, but I think an important one. Also one that is very easy to change.
 Presumably by oversight, the Marriage (Same-Sex Couples) Act 2013 does not amend this subsection to include married same-sex couples, though the 2013 Act does make consequential amendments to most other similar phrases, including in several other sections of the HFEA.