I found this a while ago on Charmouth beach. At the time, I thought it was a coprolite as it matched the description given to us fairly well, but I'm really not sure. It's about 5.5cm long. These photos don't show one of the sides, which is far rougher and looks more like a coprolite than the more polished side shown here.
I'm sure it is not coprolite. As Dan states, we can't see any food remains; but also the general appearance is one of an igneous or sedimentary rock, of which there are many types that include different a coloured fragments. To make a better ID, one would need to look at your specimen with a hand lens at least, and preferably a petrological microscope (looking to ID textures and minerals).
Pebbles on beaches can be surprisingly varied. Sometimes that reflects the variability of the rock types and soils forming the coast. But the assortment can be augmented by man, who often brings in extra material, some of which is man-made, such as brick and concrete.
It probably looks different because of the location, erosion and the tumbling which the sea has has done to it. They are quite common in Whitby but there is different rock layers in Dorset, which probably makes it less common. Also the sea will have tumbled it to make it more rounded and smooth (it probably would have started as a bigger rock.)
Nice find well done.
If we had picked your specimen up on the Holderness coast I would have said almost positivly it was of volcanic origin.
It's hard to tell though.