You didn't tell us the size of the lead cone, or put something like a coin or ruler in the photo with it to show the size. That makes it much more difficult to correctly identify.
There is a similar-looking lead cone (which has a solid base) that was one of three parts of a US civil war Shaler bullet, measuring about .56-inch in diameter. It's unlikely but not impossible that a Shaler 3-piece bullet got over to England. If the diameter of your lead cone's base doesn't measure .56-inch, it's not a Shaler bullet part.