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found on at Lyme Regis on the shore
Probably fossil sponge.
You can understand the pattern/structure you see in your speciment better if you look at the amazingly good specimen, which happens to be Ventriculites
That's from the NHM web site, but I can't link to its page directly; please go here to read the associated description - http://www.nhm.ac.uk/kids-only/earth-space/fantastic-fossils/
Fossil sponges are very common in flint. In fact there's a book 'Fossil Sponges of the Flint Nodules in the Lower Cretaceous of Texas'. I'm not suggesting you get/borrow it.
I can't sompletely rule out coral. Maybe somebody else could help decide...