Charles Frederick Thomas BURROWS was born in 1906. He married Edith M BUTLER in 1936 and they had one child living with them in September 1939, at which point he was an aircraft metal polisher.
All small number of children registered by parents named BURROWS/BUTLER in Britain between 1936 and 1939, can be ascribed to other BURROWS/BUTLER couples married close to where the children were born. As such the identity of the child in the 1939 Register remains unknown.
The principal aircraft manufacturer in Cheltenham, where Charles may have been working, was the Gloster Aircraft Company which manufactured most of the wartime production of Hawker Hurricanes and Hawker Typhoons. The company was also working on the Gloster-Whittle E.28/39 experimental aircraft and the Meteor, the RAF's first jet-powered fighter and the only Allied jet fighter put into service during the Second World War. During 1939, the company constructed 1,000 Hawker Hurricanes within the first 12 months of the conflict; Gloster delivered the last of its 2,750 Hurricanes in 1942. After ending production of the Hurricane, it was decided to manufacture the newer Hawker Typhoon in its place. Gloster proceeded to construct 3,300 in total, almost the entirety of the type.
It's possible that Charles' father, a joiner, also worked at the Gloster Aircraft Company. The company had been making aircraft and spares since the First World War, including the Gloster Gladiator biplane, but an elderly Charles Frederick senior might have been working there until he died in 1942.