I seen several times the claim than sugar was an essential nutrient for industrial revolution workers (for example this blog) and even that sugar availability made possible the industrial revolution, at least in Britain.
My (maybe wrong) understanding of these claims is that sugar became a sort of staple food for British workers. However, I can't imagine people having a bowl of sugar for lunch but I suppose a diet made mostly of bread, potatoes, vegetables and occasionally a little meat, with sweet food being mostly deserts or snacks, and even then those sweet foods are mostly composed of ingredients other than sugar, like flour. Therefore, I can't see where a large quantity of sugar fits in an industrial revolution worker diet.
Is it true that industrial revolution British working class families consumed large quantities of sugar? How did they consume it?
According to the book linked in Brian Z's answer (Syndney Mintz's classic book Sweetness and Power, chapter "Consumption", p. 149) before 1850 sugar have been mostly a sweetener for tea which added very few calories to worker's diet, but after 1850 "it appeared not only in tea and cereal but in many other foods as well and in ever-larger quantities" and it was contributing to one-sixth or per-capita caloric intake.
1/6 of daily caloric intake is 1/6 of 2000 to 2500 kcal, that is about 400 kcal, and that's a bit more than the calories in 100g sugar, which is an amount better measured with a teacup than in teaspoons.
Then the question is what the "many other foods" containing sugar that labouring families ate daily were.
For a detailed account, see Syndney Mintz's classic book Sweetness and Power, especially the chapter "Consumption". On p. 149 he mentions that by 1900, sugar "was contributing on average nearly one-sixth of per-capita caloric intake" for England as a whole, and that the portion would have been significantly higher for working-class women and children. You are correct that people were not eating bowls of sugar, but they were adding more and more sugar to a wide range of foods that did not contain them previously, mainly along the lines you mention in your question. If 1/6 doesn't seem such a big deal, keep in mind that the number was essentially zero a few centuries before.
EDIT: In response to the further elaboration of the question, here's a few relevant quotes from Mintz
The pastries, hasty puddings, jam-smeared breads, treacle puddings, biscuits, tarts, buns, and candy that turned up more and more in the English diet after 1750, and in a deluge after 1850, offered almost unlimited ways in which the sugars could be locked onto complex carbohydrates in flour form. Added sugar was customary with hot beverages, and the eating of sweetened baked foods often accompanied these drinks. The drinking of tea, coffee, or chocolate (but most commonly tea) with meals, in moments of repose snatched from work, at rising, and at bedtime spread widely. The combination of such beverages with baked goods became common as well, though not an invariable practice. (p. 133)
There is no doubt that the sucrose consumption of the poorer classes in the United Kingdom came to exceed that of the wealthier classes after 1850, once the sugar duties were equalized. Not only did sucrose-heavy foods-treacle, jams, raw sugar for tea and baking, puddings, and baked goods-come to form a bigger portion of the caloric input of the working-class diet (though probably not absorbing a larger proportion of the money spent on food), but sucrose was also an ingredient in more and more items in the daily meals. Children learned the sugar habit at a very tender age; sweetened tea was a part of every meal; jam, marmalade, or treacle figured in most. In the late nineteenth century dessert solidified into a course, sweetened condensed milk eventually became the "cream" that accompanied tea and cooked fruit, store-purchased sweet biscuits became a feature of the tea, and tea became a mark of hospitality for all classes (pp. 143-144).
He also mentions that sweetened wine and other alcoholic drinks with added sugar were uniquely popular in England (p. 136).