Thanks to you both for your detailed replies. I have been thinking this over. I have also come across a John Thompson born or baptised on 10/10/1828 in Carmeen, Co. Down, which seems to be about 2 miles from Newry. His parents names were Hugh Thompson and Elizabeth Kelly.
A coincidence? The parents' names are the same, and the place of birth 2 miles from Newry (as also stated on his wife's Poor Law application). The year of birth is, however, 9 years earlier than I expected, and the denomination is Roman Catholic.
I looked at
http://www.proni.gov.uk/guide_to_church_records.pdf for Clonallan, which is where I think Carmeen is having used some sites like Ros Davies' one. Although the above is RC, if I am looking for other denominations, there are two things I wonder about. The first is that on that link, it doesn't give any information about Presbyterian records for Clonallan - any ideas why? The second is that for the Church of Ireland records for Clonallan (which I don't think would be much use anyway as baptisms only start from 1884, it seems earlier records were destroyed), it says "in local custody". Does that mean you have to contact the local church and ask them for more information, or you have to actually turn up at the church to conduct a search of their records?
And by the way, just on the Jane English point, I know there were doubts raised before about whether English was the right maiden surname - which I originally gleaned from Annie Thomson's (MS Walker) death certificate (the informant being her son John), but English is also the MS Annie gave for her mother in her Poor Law application.
Thanks.