According to Johnson, the vaults were cleaned in 1817, and in 1841 3,250 coffins were re-stacked. No new burials were allowed after 1853. In 1859 the church wardens put ads in the newspapers asking relatives to remove coffins. After 1 Feb 1859, the remaining coffins went to St. Martin's cemetery in Camden town or they (1,857 of them ) were bricked up in three new vaults in the south-east corner of the crypt under Adelaide Street and Duncannon Street. All but 246 of them were listed by name (Johnson p. 35-36). Here Johnson cites Westminster City Archives, St Martin's Parish Records, F6102, so let's check that out!
In 1938 three thousand lead coffins and other human remains from the crypt were taken (by night) to the Brookwood cemetery in Surrey to make way for office space (Johnson p. 62).
If you're a descendant of Eliza Esdaile, you may also be a descendant of Richard Thomas who was buried in St. Martin's crypt in 1826. Richard's son George Thomas married Eliza Esdaile's granddaughter Kate Grant. I will think of the neatest way to document this and give you some citations in another post.