He was an interesting man, the royal physician and later a thriving doctor. The running joke among the Scriblerans was about the fact that he always had plenty of interesting and outlandish ideas to write about and was more than willing to give those ideas away. All accounts paint him as a funny, witty man, generous and good company. It seems clear that he didn't think of himself heavily as a literary man and it is sometimes hard to know which parts of the Scribleran body of work are his or not.
If 'John Bull' is anything to go by, then I would suggest that any part of Scribleran literature that involves long lists of things must be an Arbuthnot one. He really does love his lists. There was one chapter that consisted only of a list of various legal services. I imagine the last chapter of the 'Memoirs of Martinus Scriblerus' was probably one of his too, as he seems to be an ideas person and likes the format of lots of silly little ideas that have not been completely developed.
John Bull itself came out as three pamphlets before being collected in book form. They tell of the trouble that occurred to John Bull when he set out to sue Louis Baboon for his tailoring contracts and got greatly in debt while his lawyer, Henry Hocus and his business partner, Nicholas Frog do well. This storyline is a thinly told story of the War of Spanish Succession, with Nicholas Frog as Holland (confusing I know), Louis Baboon (AKA Bourbon) as France and Henry Hocus as the Duke of Marlborough.
Later episodes include the harsh treatment of John's sister Peg (Scotland) and her love of a young man (representing Presbyterianism) who starts pious but then tries to make Peg's Mum (Anglicanism) ill. The story also talks about the death of John's skittish former wife and his remarriage to a more sensible one - this being an analogy for changing parliaments.
Much of the humour of the book has evaporated. A topical political allegory loses much of its laughs and punches when the things it is satirising are so fixed to their time. All we are left with is a mildly entertaining story about a foolish but loveable man who nearly bankrupts himself in suing someone else.
Of course the main legacy of the book is the character of John Bull, the stoic, no-nonsense, hard-living representation of England. You don't hear so much about John Bull anymore and I imagine he is not how the English would like to represent themselves - however, some of his qualities have been invested in that icon of steadfast Britishness, the bulldog.
So, not all that recommended, although I am interested in reading a biography of John Arbuthnot some time, he's an interesting fella.