The most recent electoral registers I can find online for the area are from the 1920s up to 1931. Rouncil Lane was then known as Roundshill Lane. In 1926 the following people were recorded at Fern Hill Farm: Philip Bottrill, Elsie Bottrill and James Roberts (see image below).
In the subsequent years, Fern Hill Farm does not appear and there's no sign of the Bottrills. As you can see in the image below, in 1926 Fern Hill Farm is listed between Little Woodcote and Bulkington. When looking at the later registers, between Little Woodcote and Bulkington Cottages there are some residences just marked Fern Hill (with 4 separate families residing there), then Brook Cottages (2 families) then Roundshill Lane Farm (see below), followed by Woodcote Lodge (2 families), The Kennels (7 families) then Bulkington Cottages. Might Fern Hill Farm have become Roundshill Lane Farm? (see new posting below) In case this was the case, the occupants in 1930 were Thomas and Mary Bostock, who also owned New House Farm in Weston under Weatherley. There is one other entry in the 1930 registers which is odd. A Frederick Stanyer is noted as owning land at Fern Hill but his abode is shown as Fernhill Farm, Old Park, Warwickshire. I have no idea where Old Park is in relation to Roundshill Lane so don't know if this is significant. Obviously with your local knowledge you may be able to make more sense of all this.
For later electoral registers you will probably need to visit the Warwickshire County Records Office, although obviously you should check first to find out what they hold.
