Hi Valtaya,
I could not leave you waiting so went into Nottingham RO this morning and had a wee look for your Thomas Mee / Horton.
His grave number is 19333, and internment number was actually 85971. The trail in finding him was a bit confusing as I had to go through a massive collection of listed internment numbers. The grave number 19333 brought up a list of seven internment numbers, which I matched to the following people.
6780 - Elizabeth Lowe, spinster of Back Lane, Nottingham, died aged 32 on 28/01/1850 and buried 03/02/1850.
40057 - Valentine Henry Withers, son of Valentine and Mary Withers of Crocus Street, Nottingham, aged 7 months. Died 16/04/1882, buried on 19/04/1882.
41491 - Henry Ashton, son of Mary Ann Ashton of Riley's Yard, Canal Street, Nottingham, aged 1 month. Died 24/02/1883, buried 01/03/1883. Oddly enough I walk past Canal Street to get to the Archives.
62384 - Gertrude Ellis, daughter of Joseph Thomas Ellis of 5 Pa____ts Yard, Broad Street, Nottingham, aged 4 years. Died 20/11/1898, buried 24/11/1898
62384 - Florence Ellis, daughter of Joseph Ellis (presumably the same as above) of 5 Pa____ts Yard, Broad Street, Nottingham. Died 26/11/1898, buried 30/11/1898.
67620 - (this entry was very hard to read) Nellie Elizabeth Bingham, daughter of (maybe) James Bingham, aged 17 months. Died 25/07/1903, burial date illegible.
85971 - Thomas Mee (Norton) of 429 Hollingham Road (?), a soldier, aged 39 years. Died 01/03/1920, buried 06/03/1920.
I think the 6/19333 you refer to was taken from a number 6 that is written in the date column of the registers. The grave number is 19333.
These seven internment numbers all had the grave number of 19333, I doubled checked them all. Do you know who any of these people are? In the list of internment numbers of this grave the word BINGHAM was written, which may mean the Bingham family owned the plot, but I am not sure. I could try and find out who owned the grave if you like.
Also, the fact Thomas is listed as a soldier is interesting, dying two years after the First World War ended. Was he wounded? I checked on the CWGC site but no obvious match was returned for him.
Sad to say I think it is unlikely he will have a headstone, and if the grave does, I imagine it will not bare his name. However, I'll keep my finger on this and will see what I can turn up tomorrow (I can pop in for half an hour after uni).
I hope this helps, it looks like his family may be buried elsewhere
Matt.