Don't know if you are still searching for the UK side of the Frith family. According to the Great Marlow Baptisms there is a Charles Frith baptised 27/7/1828. Parents were James & Elizabeth Frith.
There are many Frith baptisms in Great Marlow but I have checked 1814-1847 and can't see any more with James & Elizabeth as parents. There is an Eliza in 1822 with parents listed as James & Mary???? As I said though there are lots of Frith baptisms so I could have missed one or two.