Arne's father and grandfather were both upholsterers and both became officials of the City Company of Upholsterers. His grandfather unfortunately fell upon hard times and died in the Marshalsea prison for debtors. Arne's father on the other hand earned enough money not only to rent a large house in Covent Garden but also to have his son Thomas educated at Eton College. But later in life he also managed to lose most of his wealth and had to earn extra cash by acting as a numberer of the boxes at Drury Lane Theatre.

The young Arne was so keen on music that he smuggled a spinet into his room and, dampening the sounds with his handkerchief, would secretly practise during the night while the rest of the family slept. He also, according to the musical historian Charles Burney (1726-1814), dressed up as a liveryman in order to gain access to the gallery of the Italian Opera. It was at the opera that Arne first met the musician and composer Michael Festing (d.1752).

Festing was a major influence on Arne. He not only taught him to play the violin but also took him to various musical events including going to hear Roseingrave compete for the post of organist at Hanover Square and a visit to Oxford in 1733 to hear Handel's opera 'Athalia'.

Upon leaving school the future composer was articled to a solicitor for three years. However, according to Burney, Arne's father discovered his son leading a group of musicians at what was probably one of Festing's musical gatherings. Following this disclosure of his son's real interest and talent he was persuaded (again probably by Festing) to allow the young Arne to give up his legal career and to pursue music as a living.

Arne was to suffer from one disadvantage; as a Roman Catholic he was debarred from many of the professional musical appointments open to others such as a Cathedral Organist or Master of the King's Band of Musick.