I wonder how much was actually noted on forms? If a child worked many hours but also went to school occasionally they might be recorded as a scholar.
The census entry "scholar" meant that a child was "receiving regular instruction", but it was used broadly for all children because the term is so vague. Half an hour a week counting beads or learning the alphabet could be classed as "regular instruction".
Compulsory education (England and Wales) for 5 to 10 years old wasn't brought in until the 1880's but even then, some children still worked half the day and this continued until after the war.
The Factory Acts only applied to the mills, other industries had to wait for their own specific legislation.
The Report of the Children’s Employment Commission
(1839-42) led to the 1842 Coal Mines Act and further acts for factories/other industries
The commission had found that
"...instances occur in which Children are taken into these mines to work as early as four years of age, sometimes at five, and between five and six, not unfrequently between six and seven, and often from seven to eight, while from eight to nine is the ordinary age at which employment in these mines commences.
That a very large proportion of the persons employed in carrying on the work of these mines is under thirteen and eighteen.
That in several districts female Children begin work in these mines at the same early ages as the males."The reports of the royal commissions into child labour are available to read online, usually in sections titled by district or county
The commissioners also took artists with them into the mines and factories to sketch the conditions. These are the drawings we see now when we google Victorian child labour. The children in the drawings were real people. The very same children we see on the 1841 census

At 13 he would have been expected to work to support himself.
Just as an example, the 1833 Factory Act stated children aged 9 to 13 should not work more than nine hours a day.
Unfortunately the mill/factory owners found a way around the 1833 Factory Act by using split shifts.
https://en.wikipedia.org/wiki/Factory_ActsThe 1833 Act had hoped that two sets of children would be employed and each work a full half-day (the 'true relay' system, which left the other halfday free for education). Instead, some mills operated a 'false relay' system in which the protected persons worked split shifts...an inspector (or other millowners) could relatively easily monitor the hours a mill ran; it was much more difficult if not impossible to check the hours worked by an individual (as an inspector observed "the lights in the window will discover the one but not the other")
...The key provisions of the 1850 Act were :[1]
Women and young persons could only work from 6 a.m. to 6 p.m. or - in winter, and subject to approval by a factory inspector-[98] :43 7 a.m. to 7 p.m.: since they were to be allowed 90 minutes total breaks during the day, the maximum hours worked per day increased to 10.5
All work would end on Saturday at 2 p.m.
The work week was extended from 58 hours to 60 hours.
Children (8-13) were not covered by this Act: it had been the deliberate intention of the 1833 Act that a mill might use two sets of children on a relay system and the obvious method of doing so did not require split shifts. A further Act of 1853 set similar limits on the hours within which children might work.
...in 1861 a gg-grandfather who at 13 was a "brickmaker's labourer" which sounds pretty hard
This is a drawing of child labourers in a brick works somewhere in England, I think either 1871 or 1881
