I would follow thru with a visit to City Road and follow the instructions that are in the notes column.....then.... let them know in the office that there is a problem and let them sort it out.
If you look at the page I sent you I can see where the error is but it doesn't help find the burial spot.
The number in the order book is 4468 and then look across at Number of Grave it also reads 4468. It shouldn't be.
I would suggest that they (City Rd) look in the T section for another burial taking place on the 19th May 1888. I would say its the Registrar that made the error as its all in his writing.
Burkinshaw, May (child, age 12d).
Died at 21 Warburton Square; Buried on May 19, 1888 in Consecrated ground;
Grave Number 13446, Section Y of City Road Cemetery, Sheffield.
Parent or Next of Kin if Available: Fredk Burkinshaw. Remarks: .
Plot Owner: ~ ~ of ~. Page No 390