Is this a claw or a horn?

Is this a claw or a horn?

Observation - Is this a claw or a horn? - UK and Ireland. Description: It is a bone-like claw(?) that my daughter found on a pebble beach on Mull, Scotland. It is white at the base and then it becomes grey/blue about a third of the way up, continuing towards the tip. The base has a very distinctive shape as shown in the

It is a "bone-like" "claw"(?) that my daughter found on a pebble beach on Mull, Scotland. It is white at the base and then it becomes grey/blue about a third of the way up, continuing towards the tip.
The base has a very distinctive shape as shown in the photo.
The dimensions are - The Base - 30mm x 13mm (18mm at projections); The Height 59mm.