Admiral Fox

Hello everyone, wandering if you can help me..
I work at Southsea Castle in Portsmouth which is a Tudor castle.
It was modified in 1814 by Major General Benjamin Fisher.
In the 1820s a lighthouse was added and a weathervane was added.
It always puzzled us at the museum as the weathervane is a fox because, being by the sea, it should be of a sea theme(ship, anchor etc).
After much research, I have found out that it is a fox "in memory of Admiral Fox."
Now, I cannot find who/which Admiral Fox this is. Mainly because there are so many Admiral foxes.
Can anyone shed any light??
I know it sounds like a tall order but I just need someone with a record of an Admiral Fox, probably with Links to Portsmouth, died around 1820.
Thank you very much.