I can't help but think that this question is somewhat anachronistic.
The date of the baptism is 1826. Consider that at that time:
- The modern postal system was still in the future. No stamps, though there was a post office.
- The Catholic Church was still, in effect, an illegal organization. This affected record keeping. No records in many parishes.
- No Catholic directories to look up priests/addresses.
- Did Catholic priests perform marriages in England in this period? Technically "illegal" of course, but did they? In which case did they keep records? Catholic priests in Ireland did perform supposedly "illegal" marriages.
- I doubt those married were routinely given any written certificate? Even if they got one, would they keep it, as most people were illiterate anyway.
- Modern requirements about notifying parish of baptism, etc. were far in the future (as Sinann has reminded us).