There is a slightly different version in Henry S. Simmonds, All about Battersea, which updates the story:
On the road to Wandsworth and facing Plough Lane was "Ye Plough Inn," erected A.D. 1701. In front of this Inn grew an oak to which an iron ring was fastened, and it is supposed that here Dick Turpin the notorious highwayman occasionally reined up his bonny black mare.
When the Inn was re-built in 1875-6 the trunk was removed to the front of the "Old House" in Plough Lane, which formerly belonged to Mr. Carter, who owned extensive market gardens about here.
The following lines were written in commemoration of the famous Old Plough Tree, and the present landlord has had the lines enframed for his customers to read:
"This stump the remains of the Old Oak Tree,
That flourish'd when knights of the road roamed free,
When bands of lawless yet chivalrous knights
Struck fear to the hearts of purse-proud wights!
This gay old king of the forest's wilds,
His proud head bow'd to the sun's bright smiles,
In glorious prime when his branches were strong
As shoulders of Atlas in time long gone!
His leaves in the murmuring breeze did fling
Their sweet green shade o'er the Old Plough Inn!
When the knights of the road of their deeds did sing,
'Twas there to his side was first fixed the ring
To which Dick Turpin the gallant and bold
When going to the Plough to spend his bright gold
Did tether his mare, swift Bonny Black Bess.
When rider and horse stopp'd here to get rest.
Removed from his place when the Old Plough's head
By time's fell decree in ruin was laid!
This stump that remains of the Old Plough tree
In front of 'The Old House,' in Plough Lane you may see.
Here placed in memory of the Old Plough Inn
An aged memento of things that have been!
Here in his last stage, sapped branchless and grey,
Here in cool September, the trunk's first day,
In the year eighteen hundred and seventy-six,
Was planted by Messrs. J. Goodman and Wilkes.
William Holloway.
[Source: The Project Gutenberg eBook of All About Battersea.]