Guardianship is governed by the Guardianship Act 1987.
Please note that a guardian is empowered to make lifestyle and medical decisions for the person; they cannot deal with assets or other financial matters, for that you need a power of attorney.
s6 allows an adult person to point someone as their guardian - so, the easiest way to become a guardian is to be appointed willingly by the person.
It is important to note that normal guardianship automatically lapses if the person becomes legally incompetent so, if the intention is for the guardianship to continue in those circumstances, it must be an enduring guardianship. This is, and should be, a normal part of estate planning - I have enduring guardianships and enduring powers of attorney over my wife, parents, and (adult) children and vice-versa - that way if something happens to any of us, someone can immediately make legal decisions.
Guardianship orders fall under Division 3 of the Act and, in particular, s14:
14 Tribunal may make guardianship orders
(1) If, after conducting a hearing into any application made to it for a guardianship order in respect of a person, the Tribunal is satisfied that the person is a person in need of a guardian, it may make a guardianship order in respect of the person.
(2) In considering whether or not to make a guardianship order in respect of a person, the Tribunal shall have regard to—
(a) the views (if any) of—
(i) the person, and
(ii) the person’s spouse, if any, if the relationship between the person and the spouse is close and continuing, and
(iii) the person, if any, who has care of the person,
(b) the importance of preserving the person’s existing family relationships,
(c) the importance of preserving the person’s particular cultural and linguistic environments, and
(d) the practicability of services being provided to the person without the need for the making of such an order.
Division 3A empowers the Tribunal to make financial management orders (i.e. covering those things covered by powers of attorney). In addition, the Supreme Court has powers under the Supreme Court Act to make similar orders and these, naturally, override the Tribunal if exercised.
The question the Tribunal is fundamentally concerned with is if "the person is a person in need of a guardian"? That is, is the person capable of caring for themselves?
On the face of it, having an imaginary child is not evidence that the person cannot care for themselves.