My grandfather asked me to ask “those online people” what these could be, can you help please?

[KingSepron]

He’s had these fossils for a while, he’s convinced he collected them himself, and he’s never collected outside the UK so they must have been from here.

[KingSepron]

My cat obsessively licks my fingers whenever i touch this, which is very unlike her.

[KingSepron]

And here’s better photos of the second one

[KingSepron]

Underneath

[KingSepron]

On the bottom right of the fossil on this pic shows the interesting texture that drew my attention

[Rockwood]

I think the kitty lick is an internal mold of a bivalve.

The other must be spongy bone, or perhaps even a bone cartilage gradient. 

[Calli99]

To me the first one looks a bit like Nypa burtini, a palm fruit.

[KingSepron]

Thanks! Is there anything i could do to help with the ID?

[Rockwood]

2 hours ago, KingSepron said:

Thanks! Is there anything i could do to help with the ID?

A closer look is always a help if you can do it. More pixels, cropped image or the like.

I'm doubting my first assessment now. 

[KingSepron]

Better photos of the first one

[KingSepron]

Cat lick one

[KingSepron]

[Rockwood]

Now I can confidently say that I do not know.

If this could be from the London clay the knowledge might be useful to someone familiar with it. 

[Ludwigia]

I think that the cat lick one is a strongly weathered bivalve shell. Maybe the cat liked the salt on it if it came from a beach.

[KingSepron]

I’m gonna have access to a microscope for a short time soon, would there be any way to use that to help?