The parish records, including the burial register for Highfield Church (formally known as Christ Church, Portswood) are kept at Southampton City Archives.
The burial register is described as "Burials in the district of Portswood in the parish of South Stoneham in the county of Southampton". It is just one volume but I have transcribed it in two parts.
Highfield churchyard was only active as a burial ground between 1850 and 1866 although a few were buried after this date. These later burials were generally related to family plots or significant local individuals and they are included in the burials list.
Below are links to download a pdf version of the transcript for the churchyard burials, sorted either by date or by name for ease.
After this date the register continues to include those for whom services were held, but were not buried in the churchyard. It covers the period of 1867 to 1881 and was stopped shortly after Reverend Edgar Silver arrived. The majority of pages state that the burials took place at Southampton Cemetery, now referred to as Southampton Old Cemetery. A few pages (70, 71 and 77-81) do not list where the individuals were buried but this was probably an oversight. South Stoneham Cemetery did not open until 1905.