He was articled to Charles Henry Driver (1832–1900), whose offices were at 7 Parliament Street, London SW1, and who is best known as the architect for the Victoria Embankment and Abbey Mills.
Most of his work is in London, although he also designed banks, a community centre and library at Cowfold in Sussex and St James's church at Littlehampton.
Wheeler had previously built a similar house on the same street, at number 151, for Sir Coutts Lindsay, founder of the Grosvenor Gallery, which was the main showroom for artists of the aesthetic movement such as Whistler.
In 1896 he designed an electricity transformer sub-station adjacent to the Roman Catholic church at the junction of Tooting Bec Gardens and Streatham High Road in Lambeth.
In 1897 Wheeler was commissioned by Sir Henry Harben, President of the Prudential Assurance Co., to design a convalescence home on the sea front at Rustington, Sussex.
As well as St Paul's Studios, one of Wheeler's finest buildings is the Mount Vernon Hospital, Northwood, Middlesex (still intact) (1902–04) and an associated chapel which incorporates Art Nouveau designs and motifs.
[citation needed] Altered/extended: Holy Innocents Church, Southwater, West Sussex, was built in 1848 to a design by James Park Harrison (1817–1902) of London.
In 1909 work commenced on the construction of a new vestry to the south of the chancel in accordance with plans prepared by local architects, Wheeler & Godman.
His grandson Stephen Attwood Trevor Wheeler was also an established architect, responsible for many shopping arcades, cinemas, banks and some grand and multiple occupancy houses in Surrey.