As @PreFabBroadBean said,
"I looked at the Essex Record Office catalogue, and couldn't see the burial register for the cemetery listed, but I may have missed it. There was the burial register for the Anglican church that seems to have used the cemetery from 1855, but I hadn't got a sub to see it."
The cemetery covers the two adjacent parishes that used the cemetery after 1855; All Saints and St Mary the Virgin.
On the website for the Essex Records Office they have the Burial Register for All Saints 1855-1902 (D/P 201/1/15) and the Burial Register for St Mary 1813-1879 (D/P 132/1/12)
You need a subscription to view them online (£20 for one day) or you would need to visit the records office in person in Chelmsford.
However, there are transcripts available on Ancestry and FindMyPast covering this period.
Looking at the transcripts, there were 61 people buried in Maldon cemetery in 1878. They all have a name.
.
.
Although, just maybe, I do have an idea. It may possibly be the grave of Alice Williams, who died aged 14 months and was buried on 29th August 1878.
There is no recorded headstone for her on the Findagrave site. I wonder if this was an unmarked grave or perhaps just had a simple wooden memorial?
Or the dates may well just be a coincidence, we will never know.
There is a record of an Alice Williams being born in Maldon to Edward and Harriett on 19 June 1877 and then being baptised on 29 July.
It is likely that it was this Alice Williams that died in August 1878. Although, could it also be her in this grave?