My money is on Woodcroft Park being the name of the area in the centre of Bert's map. The small buildings marked B.M.138.1 were actually the remaining outbuildings of a house or farm named Woodcroft that stood just to the south-west, but which had been demolished by the time of the large scale 1891 OS town plan. If the former grounds of the house were afterwards used as playing fields, perhaps the outbuildings were retained for use as changing rooms?
Unfortunately none of the OS maps of the area record the name Woodcroft Park, but given the lengthy gaps between the various map editions and the fact that they were produced 'down south' in Southampton, it's not unusual for local, short-lived names and ephemeral structures such as wooden grandstands to go unrecorded; it appears that the playing fields were only in use for about 10 years, until presumably the construction of Woodcroft Road and the neighbouring streets covered the site.
Description: Woodcroft area in the 1850s
Description: Woodcroft 1891