Registration district for Hythe was Elham, so have you seen this one?
Deaths March qtr 1848
Elham, vol 5 page 130
Chalke, William

There is a death notice in The Morning Chronicle, Friday 28 January 1848
On the 21st instant, at his residence, Hythe, Kent, Mr. William
Chalk, formerly of Milton Chapel, near Canterbury, aged 79

John