Hi achooo
I had a look at the church's website, the LMA catalogue and the parish registers.
http://search.lma.gov.uk/LMA_DOC/P82_AND.PDFIt would seem that the churchyard was finally closed in December 1855. It's also possible that approx. 25,000 were buried between 1813 and 1855.
Then, due to the construction of the Holborn Viaduct, the remains of those buried in the northern section of the churchyard where the viaduct was constructed were removed to the City of London cemetery in Ilford.
http://www.standrewholborn.org.uk/index.php?page=teulonThe LMA catalogue also makes reference to a burial ground in Grays Inn Road. This appears to have been annexed to Holy Trinity, which has separate burial registers. It is possible that if your ancestor was poor and died in Holborn's workhouse, they may have been buried in Grays Inn Road, but those entries usually appear in the Holy Trinity register.
Unfortunately what I couldn't see in the catalogue was a burial day book where fees paid and locations were noted.
With the passage of time, the lack of surviving records and the extreme development and redevelopment of the area I think you are unlikely to establish exactly where the burial was. If the grave you seek was of someone of extreme wealth and standing in society, then a burial in the crypt would have been a possibility. Those that could afford to, also paid for their loved ones to be buried nearer the church. Graves next to the church commanded a higher price.
If you look at the church on google maps satellite view, you will see that very little of the churchyard remains today.
I have several relatives who were buried in St Marylebone churchyard from 1820-1850. The location of their remains falls into the same scenario. I assume they may have been moved to Brookwood cemetery when that churchyard was redeveloped but they could still be there. Knowing that the family had little in the way of capital means that no headstone exists and the funerals would have been extremely basic in their nature. It is highly unlikely their coffins had name plates which could have been used for identification purposes.
Dawn