John and Eliza Dagan do not appear to have had any other children besides Edward in 1828 and I seriously think you need to check the original baptism to see what occupation is given for John before you can dismiss it.
It would seem to me that either 'Deggan' may not be the original spelling of the surname or, if it is, that father John was of Irish extraction (which doesn't preclude him being a 'Gentleman').
As Clifton, Bristol baptisms are online and the only likely entry is for said 'Edward Dagan', in '1828', with father a 'John' and mother Eliza, all 3 (with that spelling) never to be seen again in available online records this seems an extremely strong contender for your Edward. This is why you need to establish the given occupation for John on the baptism record before rejecting it.
With a dearth of 'Deggan's in UK civil registration records (and most of these descend from your Edward) it's clearly due to either a spelling difference or back to Ireland perhaps. John could have been at Bristol (a port) because of business of some kind where Edward was born and they later returned to Ireland.
There is no Edward Deggan baptism anywhere in England, let alone Bristol, and the only likely entry is indeed in Bristol and just happens to be right forename, right date, right father with a soundalike surname??? All 3 than vanishing??
Don't see how you reject without further investigation.
Annette