The most likely baptism I found for Michael Riordan was in Soho Square, Westminster, Middlesex. Birth date 14 Jan 1816 Baptism date 21 Jan 1816
There is also a Honora Riorden (that is the transcribed spelling? unsure why) in 1813.
The age listed on the other documents matched the date of baptism, so it is likely the baptism I found online and posted previously is the same one mentioned on Thomas Marlow admission report?