It weighs 19g. Feels quite light. Strange texture, not smooth like stone but looks as if stone has formed around it. Ridge running from top to bottom. Sounds like stone if tapped on glass?
Found in garden. Minster kent
Please show us a photo of the broken end, ideally a bit sharper than you other photos - I'm looking for cellular structure that might indicate bone/antler/tooth.
Also, how heavy and hard does it feel?
Basically - heavy and hard like rock, or light and a bit softer like bone?
The photo of the broken end looks just like stone to me, in particular it is reminiscent of flint. The density of flint can be as low as 2.57 (google search not my knowledge) which is quite light for a rock. It is as if it has cast the insider of something and then this something has completely eroded away. Mike is good with rock!
I am sure, from the end-on photo, it is composed of flint.
I suspect it may be a fossil billfish rostrum (Xiphiorhynchus sp.)
Search for Xiphiorhynchus on this page
(I can't put a link to it directly)
Minster is mainly on the London Clay (Palaeogene, 34-56m years ago), which has yielded fossils of billfish
Your specimen is of flint, so it may have been brought-in from the chalk, not too far away to the south, and would be older.
There are undoubtedly other possibilities, eg. Cylindracanthus (but that tends to be well-ribbed, unlike yours).
For general info on the Minster area, see http://www.minster.ukfossils.co.uk/
(which happens not to mention Xiphiod fishes).