First thing I think is for her to stabilise her drinking in the sense that she is drinking the same amount of units every day. Do you have an idea of how many units she is drinking a day?
It is safe to self reduce but by no more than a max of 10% per day, and if she has a history of withdrawal related seizures or hallucinations she needs to be particularly cautious.
Generally, drug and alcohol services are more interested in showing good engagement and commitment to recovery to offer in patient detox rather than needing to reduce first in the community. Does the service offer groups etc that she can attend to demonstrate her commitment to recovery? In patient detoxes are expensive so they won't be offered unless someone can demonstrate they are ready.
Drug and alcohol services also usually offer ambulatory detoxes where appropriate (so home detoxes where you are given the medication to take at home and monitored by home visits and/or appts at the service). Community detoxes are generally only appropriate if there aren't other complexities, for instance liver disease, serious mental health problems, or history of seizures. Could this be something she could explore as it's cheaper for services so generally easier to access. If she lives on her own or can't sort childcare etc this wouldn't be an option.
Having said all this, getting a medically assisted detox is only a small part of recovery, but one that people often focus on. There is no point in having a detox unless she works on how she will remain alcohol free after. Things that seem to support this are meaningful use of time/structure to days whether it be work, volunteering, exercise, hobbies etc, supportive family/friends, attending groups whether it be AA or another style of peer led support, accessing mental health support if this is an underlying issue, some people find disulfiram helps if this is appropriate and alcohol services are willing to prescribe.
I hope that your friend is able to move forward with her problems, I wish her the all the best.