His early appetite for constant and varied amusement is captured in the double portrait by Joseph Highmore of 1743, which portrays his brother Pen seeking to study while the young Wadham attempts to draw him into the garden, tennis racket in hand.
In the summer of 1768 he contrived to absent himself from his battalion duties at the Tower of London in order to enjoy Ascot with his cousins the William Pitts of Kingston, a few days later entertaining his aunt Barbara Wyndham by taking her to Vauxhall and Ranelagh.
However, later in the same year George III's summer review of all regiments in England prevented him from attending the Salisbury races where his cousin William Wyndham of Dinton was a steward.
He reached home, however, in time to stay with the Portmans at Bryanston for the Blandford Races and to accompany his father on 12 August to their Exton estate for the shooting season.
He had purchased a house in Charlotte Street, Bloomsbury, London, in 1771, and with his wife Sarah, née Leander, (they were married at St George's, Hanover Square on 14 December 1812) he had three sons and six daughters.