I doubt he would get PR. I have a relative who did the, "Prove it's mine" thing.
What he didn't know was that meant HE had to pay for the test. That's about £400 now.
Trying to get PR is what you are really worried about, not the BC. If he wants that he would have to go to court and that is another couple of hundred £.
BUT you also get to have your say. And PR is just that, responsibility, so he would need to provide a home for his child, which will probably involve paying some of your rent / mortgage.
You obviously know him best and I would take legal advice but think about what you want for your child.
Would you be OK if the father made a one off payment and you both agree he will have no further contact and you will not ask him for CSA payments?
Why would someone pay money toward a child they have zero parental rights for?
Because it is your child. As a taxpayer I, and you, pay financial support for many many children we have no PR for.