I've found very few references to this trade myself other than the two turned up by my distant cousin Frank Gander. First, in Life and Labour of the People of London by Charles Booth, published in 1903, there's a detailed description of hoop benders and their work as follows:-
"These are a very small body of men in London. There are certainly not 50 of them. The largest house in the trade has not more than 8 workmen. All those employed are men and their business is to bend split wood into hoops to put round casks or barrels either as truss hoops or to cover iron ones, or in some cases as a substitute for iron. Underwood, generally hazel or ash of ten years growth, is cut by the woodman and assorted for length and then handed over to other country labourers to split and shave. After this it is ready for the benders, and comes to London (and elsewhere) in bundles of different sizes known as "Fourteen feets," "Middlings," "Longpipe," "Shortpipe,'' "Hogshead" (which are used chiefly for sugar casks and packing hogsheads) and other sizes known as "Barrel," "Kilderkin," "Firkin," "Long Pink" "Five feets," "Short pink," "Tambril," "Threes," "Twos," and "Ones" - referring to three, two or one gallon casks - for use in dry and tight work of every sort. The hoop bender at work chooses out two lengths of wood and bends them together between ' Hoop-bending is hard work, and the men must have strong arms, and know by experience how much strain a given piece of wood will bear ' a pair of iron jaws until they fit inside a standard hoop called a "shive", then the ends are fixed with wire or twigs, and the hoop is ready for use. The actual bending is generally hand-work, but is sometimes done by machinery. All work is done on piece, Winter is more busy than summer to supply the demands of coopers on new work, but employment generally is rather casual, and there are several men who do other work and only come back to bending when that is brisk. Hoop-bending is hard work, and the men must have strong arms, and know by experience how much strain a given piece of wood will bear. An average man in a regular situation will earn 28s per week. In slack times if a man can get employment at all he must not expect more than 15s, or half a week's work, but, when very busy, a young and fast worker has been known to make over 40s. 1854 was the annus mirabilis for both coopers and benders, so much merchandise of one kind or other being then packed in barrels and sent off to the Crimea."
There is at least one earlier reference describing coopers and their work which includes the following details of the fitting and functions of the different kinds of hoop but without actually naming 'Hoop Benders' as such. Again found by Frank Gander. This is an extract from an article by Henry Mayhew in the Morning Chronicle newspaper of 12th September 1850:
"The trade of the cooper is divided into wet, dry, white and general coopers. The wet (or tight) cooper makes every kind of vessel used for the reception of liquids. The dry cooper, on the other hand, makes the casks used to contain dry goods and packages generally. The white cooper forms tubs, pails, churns, and similar articles, while the block or general cooper, is practised in all of these branches."
After describing the selection and skilful shaping and jointing of the staves in 'making a wet or tight cast', he continues:
"The staves being thus 'jointed' or prepared, are fitted one to another round a block; a 'head hoop' afterwards encircling them, and holding them all in one round. 'Truss hoops' are then applied, which are strong wooden hoops, holding the staves firmly together until the iron hoops can be affixed. Before affixing the iron hoops, however, a fire made of chips and shavings lighted in a cresset, or small iron grate, is placed within the staves, so as to make them tough by warming the sap, and thus get them to bend without cracking. To this 'firing' the closest attention must be given, for if it be prolonged beyond the exact time, the staves are rendered brittle instead of tough. As soon as the cask is sufficiently fired an 'over runner' is put round the staves; this overrunner is a very strong wooden hoop, and is driven down by the cooper's 'trussing adze' the upper part of the cask being first bent close together. The lower ends of the staves distend through the action of the heat, but the overrunner is driven gradually down to the 'bouge'; to effect this in large and strong work the cooper calls out, 'Truss, oh!' and immediately two or three of his fellows come to his aid, and drive the overrunner down so as to compress the staves sufficiently and reduce the distention. The cask is then prepared with tools called 'chimes', used for 'sloping' the ends of the staves, and grooves are made for fitting in 'the heads'; this being done, the hoops are affixed, and the cask is then complete, All 'wet' casks are made in the same way, and are iron-bound as a rule; vinegar casks, however, are an exception, for they are bound with 'twigged hoops', that is to say with hoops twisted round with twigs, the hoops being of hazel, and the twigs or overlapping part, of willow."