This may be a name transferred from Glenhead which is around two miles to the South West. 

Name shown on historic map of Larbert.

The early maps identify the area as dedicated to Coal Mining and there was a Meldrum Pit locally

Avon Hall was built in 1878 to the design of James M MacLaren for the timber merchant John Fairley.   It was restored in 2019.

The gardens are part of the grounds of the Oak Inn (later the Royal Oak Hotel) dating back to the mid 19th century.  It was converted into two town houses.

John Tait was a distinguished Boys Brigade stalwart and a local historian of Bainsford and Grahamston.  He was a Senior Elder at Bainsford Church and long time treasurer there.