It has been a few years since i fished any river, but back in the day daiwa 12′ feeder rods were spot on for bream/skimmers in the trent using open ended feeders.
Not had hold of a daiwa feeder rod for many a long day but that is the first place i’d look but any rod with a softish tip section with some back-bone lower down to aid casting will do.
Take a good look what is out there and pick one that feels right in your hands, just remember the trent is very wide in places and further out you are fishing the longer the rod you need but beware, most of the very long feeder rods on the market are a bit too powerful for skimmers.