Harwich, U.K. - coral inclusion in flint?

[FunkyMonkey]

Hi all,

Harwich in Essex, U.K. is mostly famous for The Mayflower but it does have a small beach on which sharks teeth can be found. My wife and kids were lucky to find some but I was not so lucky. I did however find this. 
Could this possibly be an inclusion of a piece of coral in a flint nodule? If so is there any way to determine species and a possible age?

Thanks in advance!

[Tidgy's Dad]

The look of the colour of the inside and outside of the nodule and its shape suggest it is a true flint from the Late Cretaceous and came out of the chalk. 

The fossil does look like a coral, but may be a type of sponge, as these are more commonly found at the centre of flint nodules. If so, the horizontal tubes would not be coral septa but the infillings of the sponge's ostia. 

Edited August 25, 2021 by Tidgy's Dad

[FunkyMonkey]

Thank you @Tidgy's Dad for such a full answer. Most appreciated!