Not every rehab works this way, and for most people rehab does not include medical detox. Mine did out of necessity, but many had been sober for a time (usually days) and insurance covered them. It's more about getting a referral from your doctor for the insurance, it's harder for them to argue coverage when it's been medically indicated. A good friend of mine who I call Nurse Jackie (she is a nurse and was caught using IV dilaudid on the job) did a week in medical detox first and then came in to a completely different rehab.
I know that years ago a friend's boyfriend had been sober for a week or so and had to do some heroin so he'd test positive on intake. I've not heard that commonly, but that's what he did. I guess you could do the same.
Try another rehab. I agree that inpatient is a preferred solution for some. I also don't know where you are, from what I've read the UK has very different rules.
Get a referral to a doctor that specializes in addiction and get them to refer you to inpatient. That will carry more weight than whether or not you are drunk at intake.
FWIW, my outpatient rehab helped me far more than inpatient, but I don't think it would have without having some distance from my drugs of choice. I got sober 5/9/17, last drink was a bottle of wine right before my ride to rehab that day. I stayed 5 weeks, then outpatient was 8/5/17.