I found this (ignore the white blobs, they are just white-tak I used to prop up the specimen for the picture) amongst flint pebbles and shingle on the shore of Southampton Water (UK).
The rough part of the outside looks and feels exactly the same as the top part of a fossil shark tooth I collected years ago; the inner psrt, exposed at the ends, is smooth and glassy-feeling. The whole specimen is very hard and flint-like.
It looks a bit like a picture of an ichthyosaur bone I saw on this page - that one was collected quite some distance from here, but there are fossils, including ichthyosaur remains, in this general region.
Sure; most of the rocks on the shore where I collected this were flints, but this one isn’t like any of them in colour - they are predominantly orange/tan and white; or texture - the outer part of this specimen has a sort of ‘greasy-smooth’ surface. the inner part is slick and glossy, unlike the inside of the flints, which is sort of porcelain-like. Also, this specimen goes ‘tick’ when tapped, where I would expect a flint of similar size and proportion to ‘tink’ or ‘chirp’ a bit.
Of course it may be just a rock, but it doesn’t really look much like anything in your links. Of course, concretions are often responsible for preserving fossils. here is a flint pebble that I picked up (at a beach a couple of miles away from the one I went to today) and very nearly threw in the sea, noticing just in time that it is the fossil of a sea urchin test (the pic doesn’t do it justice, but you can just about see five radial features).
