During the Great Plague of 1665 the whole of Uvedale's household escaped the disease, owing, it was thought, to their inhaling the vapour of vinegar poured over a red-hot brick.
In 1676 it was made a ground of complaint against Uvedale that he neglected the grammar school for his boarders, his opponents making the further charge against him of having obtained an appointment as an actor and comedian at the Theatre Royal from the lord chamberlain to protect himself from the writ of execution.
In 1696 his neighbour, Archbishop John Tillotson, appointed Uvedale to the rectory of Orpington, Kent, with the chapelry of St Mary Cray, but he appears not to have resided.
In John Nichols's Literary Illustrations are sixty letters from Uvedale to Richard Richardson of North Bierley, dated between 1695 and 1721, mainly referring to the exchange of plants.
It contains plants not only from Sherard, Richardson, Petiver, Plukenet, Robart, Rand, Dale, Doody, Sloane, and Du Bois, but also from Tournefort, Magnol, Vaillant, and other continental botanists, labelled by Uvedale.