Hi Phil,
My grandfather was Park Keeper at Farm Park from 1927 until he retired in 1953. The family lived in Lloyd House - a grand house for a park-keeper!
My father was about 12 when they moved there and he is still alive today, aged 96. By the time the family moved there in 1927, the fish pond alongside the carriage drive had already been filled and the boat house demolished. As well as Lloyd House, there were two other buildings still standing in the Park. I don't know whether either of these houses was the 'original' farm or whether that had already been demolished.
My father describes one as a building with stables and a separate coach house. The coachman to the Lloyd family (Jack Oldnall?) had the right to continue living there after the park was given to the Corporation. Part of this house was used as a mess room for the Park staff. This house had a walled garden, where my grandfather used to grow his vegetables.
The other building was lived in by a servant to the Lloyd family, Mrs Bates and her son, who was also given the right to continue living there. My father says this cottage is the one in your picture taken in 1932. This building looks like the picture of the house illustrated (and referred to) as possibly the oldest building in Birmingham in the 1906 book 'The Lloyds of Birmingham' and which was then known as Owen's Farm.
By the way, we think it might be my grandfather in the 1932 picture!
These two buildings were demolished after my grandfather retired and are now marked in the Park with a finger post and an outline of the footings.
Alan