He was educated at Eton and Christ"s College, Cambridge.
He bought the lease of a house, later named Radnor House, thought to have been constructed around 1673, in Strawberry Hill near Twickenham and is recorded as having lived there from 1722 until his death. Robartes embellished the house in Gothic Revival style and adorned the gardens with statuary. His gazebo and summer house survive in Radnor Gardens today.
Horace Walpole referred to the property as Mabland in a letter to Richard Bentley, a mocking reference to the ornate decoration of contemporary Marylebone Gardens.
Some observers conjecture that Walpole was piqued by his neighbour"s anticipation of his own architectural ambitions, as this pre-dated his embellishment of Strawberry Hill House. Alexander Pope lived nearby to the north, their two respective properties perhaps separated by one or two small intervening houses.
Robartes was a witness to Pope"s will, whilst Pope countersigned a lease for Robartes, evidence that the two were on good terms during their 22 years as neighbours. Inside the house, Robartes built a collection of art works, including Canaletto"s The Old Horse Guards from Street James"s Park now owned by the Andrew Lloyd Webber Foundation.
The collection also included work by Meindert Hobbema and paintings by Samuel Scott.
Robartes is credited as having commissioned Peter Tillemans View of Richmond from Twickenham Park, c. 1720. Robartes himself was the subject of a portrait, c. 1741, attributed to the circle of Thomas Hudson, later to become another neighbour at Cross Deep. Robartes died, a bachelor, 15 July 1757, aged 71.
With his death the titles of Earl of Radnor and Baron Robartes became extinct.
He bequeathed the house and much of his art collection to his steward, Frederick Atherton Hindley, the Canaletto and Hobemma to James Harris and two Scott paintings to Richard Owen Cambridge.