If a child under 16 is undergoing gender reassignment, or sees themselves as being a boy when physically they are a girl (or vice versa) - sometimes known as gender dysphoria - this could mean that they will not want to share a bedroom with a child of the same (original) sex.
Some have argued that until there is a physical change the child must be regarded for these purposes as their original gender - so this would be a problem for under 16s as they cannot by law have a gender change surgery - however they can start the process of reassignment before then, and this is included in the definition of Gender Reassignment under the Equality Act (see below)
There could also be an argument to make to the DWP ie that one's gender for these purposes should be however a person views themself.
The Equality Act 2010 states:
Therefore even if the additional bedroom is not allocated - because of going by the original gender - the HB Office should at least allow a DHP, on Equality grounds.
149 Public sector equality duty
(1)A public authority must, in the exercise of its functions, have due regard to the need to—
(b)advance equality of opportunity between persons who share a relevant protected characteristic and persons who do not share it;
(3)Having due regard to the need to advance equality of opportunity between persons who share a relevant protected characteristic and persons who do not share it involves having due regard, in particular, to the need to—
(a)remove or minimise disadvantages suffered by persons who share a relevant protected characteristic that are connected to that characteristic;
(b)take steps to meet the needs of persons who share a relevant protected characteristic that are different from the needs of persons who do not share it;
(7)The relevant protected characteristics are—
pregnancy and maternity;
religion or belief;
7 Gender reassignment
(1)A person has the protected characteristic of gender reassignment if the person is proposing to undergo, is undergoing or has undergone a process (or part of a process) for the purpose of reassigning the person's sex by changing physiological or other attributes of sex.