There is a Henry Bexfield [spelling slightly different] born at Yarmouth 28th April 1807 and Baptised 29th April 1807.
His parents are stated to be: Thomas Bexfield and Eleanor Quinton.
...Maybe if you are searching at around that period, you could try looking for Bexfield as well as Baxfield. I am not absolutely certain the above is your Henry, but you never know....
Hope this helps,