Contradictory information regarding enhanced disability premium (single)

Hi. I hope someone here who may have experienced the same thing will be able to advise me. In January of this year, I received a council tax reduction notice letter which had listed on it the enhanced disability premium (single) on it. This was £15.90 at the time and this amount was used in calculating my reduction. The problem was I have never received the enhanced disability premium. I queried this with the council at the time and was told that the information they used to calculate my reduction came from the job centre. I was told to pursue it with the job centre as it seemed I was entitled the premium as it had turned up on my decision letter. I didn't feel able to do this at the time. I decided to bite the bullet and try to get more information about why the premium was appearing in my council tax calculation but nowhere else. I first contacted the DWP, who suggested I go into the JobCentre and show them the council tax letter. This I did, but found the lady I spoke to completely unhelpful. She basically contradicted what I had been told by the council tax office, that it was a council tax error, essentially, and nothing to do with the JobCentre. This was a salutary reminder of just how unhelpful the gatekeepers in jobs like this often prove to be. I plan to contact the DWP again to see if I can get a definitive answer to why this is appearing on council tax letters if I'm not entitled to the premium.
I thought I would ask here before I go back to the DWP. So my question is: Am I entitled to the Enhanced Disability Premium or not? The benefits I currently receive are as follows:

I am in the support group of ESA. My benefit later states that 'because you are entitled to contribution-based ESA we will pay you £110.75.' This figure is made up of £73.10 living expenses and an extra £37.65 because I am in the support group. But the council are using a figure of £125.55 to calculate my council tax reduction, which is where the confusion has arisen. I do not receive PIP or any other add on. I have been in the support group for well over a year, if that makes any difference. I would be grateful for any advice on this matter.