We found this specimen in a small sandstone pebble on the beach near Scalby Mills just north of Scarborough. It was next to the dinosaur footprint bed in the shingle on the wave cut platform. Are we on the right track?
I don't think this is a segmented worm or centipede fossil I'm afriad - what it does appear to be is two stages of re-mineralisation of the rock, where the rock has fractured and then the cracks have been filled with the black material and then that has dehydrated and the cracks formed from that dehydration have also been filled with the white material.
It's difficult to tell without seeing the actual object, but that would be my best guess.
The black material is actually fossilized wood, not uncommon in the beds of the so called Ravenscar group that does often contain fossil plant material. As Hazel mentioned, it shrank during fossilization and the cracks were filled with what is probably calcite.