No, they have no obligation to house her as she is a single person without diagnosed health problems. She will need to get a diagnosis do be entitled to housing. But as things stand they have no obligation to house her, she would be directed to hostels or might have to rough sleep. Criteria is here but from what you say she fits none:
If you will become homeless within 28 days your local authority (council) only has to re-house you immediately if you are one of the following:
a) You are a pregnant woman, (this includes anyone living with you).
b) You have children who rely on you financially and they need somewhere to live.
c) You need special help either because you are old, mentally disabled, physically disabled or other special reason.
d) You became homeless because of a flood, fire or another disaster.
e) You are a child aged 16 or 17 and you are not in local authority care, or recently left long-term care. (In Wales 16 or 17 year olds will be regarded as in priority need, regardless of whether or not they have been in care.)
f) Any person aged 18, 19 or 20 who is at particular risk of sexual or financial exploitation, (applies to Wales only).
g) Any person who is not yet 21 years old, but who was at any time between the ages of 16 and 18 being looked after, accommodated or fostered, but are no longer. This does not apply if that person is also in full-time, further or higher education, (social services would be responsible for accommodating those students), (this applies to England only).
h) Persons aged 21 or over who have become vulnerable as a result of having been looked after, accommodated or fostered, (this applies to England only).
i) A person who is 18, 19 or 20 and who has at any time been privately fostered, lived in a children's home or been in the care of a local authority, health authority or voluntary organisation, (this applies to Wales only).
j) Any victim of any form of violence, (except self-inflicted) who has left their home as a result of violence or threats and has become vulnerable as a result, (this applies to England only).
k) Any person who has been subject to domestic violence, is at risk of domestic violence or would be if he or she returns home, (this applies to Wales only).
l) A person who formerly served in the armed forces and has been homeless since leaving those forces, (this applies to Wales only).
m) Any person who is vulnerable as a result of having been a member of the regular naval, military or air force, (this applies to England only).
n) Any person who is a former prisoner and has been homeless since leaving custody and has a local connection with the area of the local authority to whom they apply, (this applies to Wales only).
o) Any person who is vulnerable as a result of having been in custody, (this applies to England only).