This information comes from ‘The Date of the Three Shire Stones near Batheaston’ by AJH Gunstone, p210 in the Trans Brist/Glouc Arch Soc v82 (1963):
‘Most field archaeologists who have studied the site in recent years have suggested’ that the megalith was built in the early 18th century reusing stones from some ruined chambered tomb in the district, possibly the one drawn and described by Aubrey in the mid 17th century (see TBGAS 79 p1/18 for a sketch).
There are three small dressed stones inside, each dated 1736 and with the initial of one of the three counties.
“Completion of the project in February 1859 was given wide publicity in local newspapers and national journals and these reports added that in the hole excavated for the upright stone on the Gloucestershire side three skeletons and a coin of James II were found.”
And here is part of a letter referring to the newly spruced up monument:
Bath. Nov 17th 1858.
Sir.
For the last 120 years the only index to mark the junction of the 3 Counties of Gloucestershire, Somerset and Wiltshire on Bannerdown [..] consisted of three Stones of the dimensions ordinarily used for mere stones in Common field lands; and they were in such a position that travellers could not possibly be attracted by them; and that even those, who knew of their existence, could not at once discover them.
[..] it was resolved that a Cromlech should be erected over the old stones [..]
The total cost was £34 5s and 8d. I thought it was rather nice that “Dinner to the Workmen” was listed as one of the expenses.