As the other and yourself I am on the manufacturer side and never been told by a distributor that they can obtain a CFS on my behalf. And I am really happy of that as I can then control where my product is sold.
But I assume that if you provide to this distributor all the necessary documents he can request them by himself.
When I looked at the MHRA website to see if they ask only Manufacturers to request CFS, I find that the answer is NO. They tell that you can be another organization asking for the CFS on behalf of the manufacturer but you need to define your relationship.
Link
I hope this helps to move the needle.