HASAWA (health and safety law) states the number of toilets per premises and that they have to be separated by sex, not gender.
Your friend is premptong the company breaking the law.
Does the workplace have a disabled toilet? The accessible toilet is usually a gender neutral toilet.
I have worked in one work place where one of the disabled toilets was also designated a trans toilet.
Ge your friend to point out that she is also looking forward as a MTF transgender person may not be comfortable using the male toilet, particularly when they have a period.
Ask CEO how he would react to used sanitary products int he men's toilet.
Point out policies implemented by other organisations when single sex space became mixed eg when the fire brigade first recruited women then a female fire fighter could be in the sleeping space alone, she could be there with several men but not with an individual man both to protect her from and sex based violence or bullying and to protect the man from false accusations.
Under the equality act both sex and gender identity are protected. Asking the MTF trans person to use the disabled toilet is not discrimination because you also ask disabled employees to use it. In addition there is more space and usually a full length mirror so a person can check how they look before leaving, ideal for someone who may not be comfortable adjusting clothing in the communal part of the ladies.