Good morning from Down Under, Fiona,
I presume from your ancestry that you live in NZ and if so, it is a pity we hadn't made contact before your trip, as I have recently written a supplement to my book and covered a lot more on the Davy family. It includes quite a few photos including of Walter Humphrey Davy and his brothers and parents.
In case you are unaware Jonathan Davy appears in Cardiff Records as a Churchwarden of St John's Cardiff for the year 1783. He is noted in a 1795 Cardiff Trade Directory as 'Grocer & Wine-Merchant'. He died and was buried at St John's on 19.11.1798. It was his widow Mary who signed the licence for their daughter, Mary, to marry in 1806; she may be the Mary Davy who died [per FreeBMD]in Q2. 1859, Cardiff (not sure).
There are some things to seek out whilst in Glamorgan so if we were to communicate by direct email I can send you some stuff.
Please contact me on firstname.lastname@example.org