This is sounding complicated!
First thing i'd do is call up the uni and ask to speak to the First year students (freshers) Housing Advisor - all uni's will have one, its a department to help first years sort out their accommodation
On the phone, calmly explain your situation, dont give them un-necessary details, just tell them you have a child who you look after... (but who isnt your actual blood-related daughter is that right? Sorry if not its just a v confusing thread!) ... who needs first year accommodation.
Explain that you do not meet the criteria to be her guarantor as you are self employed, and her father refuses to be one. The Housing advisor will then talk through some options.
The bottom line is, a University is a business BUT they will want to help and keep this girl as a student by any means! Meaning they will help you find a solution if you calmly explain that youre looking for advice :)
It may be that she cannot stay in first year halls and has to find a shared flat to live in. In a 6-bed flat share for example, you may be looking at £300-£400 a week ish (but not knowing your location that can massively vary, London vs Teeside for example, the rent differences will be £££'s in differences)
Talk to this girl about all this, not to panic her but to let her know that she will need to help you find a solution to this - she may know some other students who are also in a pickle and can help, or she may have been given some helpful contacts and numbers in her starter pack for Uni - she needs to know the situation but it doesn't need to be full on panic just yet :)