Just twigged who you are, Draigcoch! Heavens - I'm slow sometimes!
OK - I've found the Irish Burnell family (and spelt this way) - they lived in Harp Street for the 1851 census so you were perfectly right. The whole family is recorded as being born in Ireland. They are John (66, stonecutter), wife Mary (48), Elizabeth (20), William (19, a stonecutter), Caroline (15), Samuel (13) and John (11). Given that John was born in Ireland and was only 11, they could not have arrived in Holyhead before 1841. They did not appear on the 1861 or 1871 censuses, so they probably moved on - no further appearance from them.
Oddly, I had not seen the entry for them before. But that, I believe, now closes the issue of the Irish Burnells, and we go back to wondering where Jonathan Snr came from.
Welsh Burnells in 1851 are recorded living in Hibernia Row (William Burnell b1825, Jonathan Jnr's older brother, & family) and Upper Mountain Row (Jonathan Burnall Jnr & family).
There are no other Burnells of any spelling in Holyhead in 1851.
Interestingly, the 1841 to 1871 censuses all record Jonathan Snr as being born in Holyhead (the 1841 one says "born in county" which is good enough!).
So - thoughts, please?
Cheers
Amlodhi