Record set England Roman Catholic Parish Baptisms
First name(s) Michael
Last name Riordan
Birth year 1816
Baptism year 1816
Parish Soho Square
Diocese Westminster
County Middlesex
Country England
Mother's first name(s) Honora
Mother's last name Lyne
Father's first name(s) Cornelii
Father's last name Riordan
Birth date 14 Jan 1816
Baptism date 21 Jan 1816
Church St Patrick
You said you're unsure if this was likely to be the correct Michael. You're wise to be unsure. The only evidence you have is that his mother's name was Honora. As we know, Honora was a popular name in Ireland at the time. Michael features among the most common Irish names. Riordan is a very common name. So, putting the 3 together, there may have been a lot of babies named Michael Riordan born in those years, many without baptism records.
Until you know more about Michael Riordan, e.g. country + approximate year of birth, you'll be catching red herrings. Add to that events around the possible time of his conception & birth, the end of a long major European war with serving and discharged soldiers & sailors on the move, followed by years of widespread harvest failures throughout Europe, leading to famine, unemployment, economic depression, cuts in wages, civil unrest and government fears of a revolution in Britain. It was an unstable time.
Besides all that, Michael Riordan was Catholic, or at least, the one who was baptised at St. Paul, Soho Square was. Whether your Michael Riordan was born & baptised in Ireland or England, if he was R.C. it's hit & miss if his baptism was recorded, and if it was, whether the record survived. Even if it did survive, if it was an English R.C. register, that it made it to an archive. Even if it got that far, it may never have been transcribed and therefore no transcripts online. Even if it was transcribed, some of it may have been illegible or damaged, there may have been individual entries, pages, years and even runs of years missing. I've come across all those things with my Irish and English Catholic ancestors, 18th-20th century. There's an entire decade of the early 19th century missing from the Catholic mission registers in an English town with a large R.C. population, of which my ancestors comprised a sizeable proportion, because the priest in charge was in poor health for years. Entries are missing from the years which were kept. (See Catholic Family History Society website for English Catholics and National Library of Ireland for coverage of R.C. parishes there.) Catholicism was illegal in Britain and Ireland until 1790 and it was another 40 years before Catholics gained (almost) equal rights. Even after that period England was a mission country until R.C. dioceses were set up again in 1850. Some areas without large or longstanding R.C. populations had no Catholic churches. Priests held Mass in houses or schoolrooms or rooms above pubs. They would baptise babies at home. The register would have been a notebook. They might have lost bits of paper or forgot to write things in the notebook. One of these priests was a cousin of my 2xGGF. His own baptism, around 1821 is one of those missing, and his parent's marriage and baptism of his grandmother 50 years earlier (my 4GGM).