Yes, you do and from my reading of the
Gov.UK website, you are not eligible for a refund of it either.
People working in the NHS on a Tier 2 or Skilled Worker visa and their dependents are automatically refunded their IHS after paying it. As you are on ILR, you do not meet that requirement.
If somebody working for the NHS on another visa has paid their IHS, they are eligible to be refunded the IHS for every complete six months that they work for the NHS after their visa has been granted/extended. That also applies to their dependents. As you are on ILR, you will not have paid the IHS at the time of your current visa application and hence I believe that this would not apply to you either.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.