In reply to Nathancoward:
Not sure whether you're solely interested in the history of the Whillans Harness, or harnesses in general. However:
The Whillans Harness was designed originally for prussiking and abseiling on fixed ropes on Bonington's expedition to the South Face of Annapurna in 1970; that is to say, while allowing the attachment of jumars, descendeurs, etc, it wasn't actually equipped with a rope tie-in point, the clip-in loop being low down on the crutch-strap, ie lower than desirable for rope attachment. On that particular expedition they took the Troll Chest-harness for rope attachment purposes, that model being, I think, already in existence. Troll subsequently modified the Whillans Harness into the ground-breaking conventional climbing harness that became the standard in the UK and elsewhere for a number of years. Chouinard marketed (I think) a double-buckle version of the original for a while (his business partner, and gear genius, Tom Frost was also on the Annapurna trip), but I don't know how successful it was in the US, particularly with strong competition in that area from, among others, Bill Forrest.
As others have said, the Whillans was by no means the first climbing harness, in the UK or anywhere else; it was probably, however, the first sit harness that fulfilled all the requirements of the typical climber - rope tie-in point, abseil/prussik attachment, you could hang in it without strangling, gear loops, etc. Quite a good sit harness came on the UK market a year or two before the Whillans - the Davek Harness designed and marketed, I think, by Derek Walford, possibly based in Sutton Coldfield at the time; I don't know whether he had the manufacturing capability to actually make it , or whether that was outsourced - Troll, perhaps, who better? It achieved some notice by being used by Doug Scott on the first ascent of The Scoop on Strone Ulladale (sorry; sassenach spelling!), but disappeared without trace when the Whillans hit the market. Prior to that, in the UK at least, harnesses could largely be divided into two types: those that provided a full strength attachment for the rope, and those that simply offered padding for the rope that was still tied around the waist, generally with gear loops of some sort included.
The first type tended to be chest harnesses, and possibly owe their commercial origin to the Edelrid model which was actually made of multiple-ply 9mm rope - 4-ply at first, with a presumably more comfortable 6-ply model coming later; I'm not sure when they first appeared, but Harlin and co. certainly used them on the Eiger Direct in Feb/March 1966 - as I would imagine did the German team - and memory suggests that they may be in evidence in photos taken during the first winter ascent of the Eigerwand in March 1961. I said "commercial" because I think the first climber to be credited with using a chest harness - presumably homemade - as opposed to simply tying the rope around his chest, was Raimund Schinko who was active in the limestone of northern Austria - Dachstein, Gesause, etc - in the 1930s. As I've said Troll also had a chest harness, theirs obviously made of 2-inch webbing, as did Davek (as well as the sit harness); Edelweiss also produced a rope-based model, but I think that came later; as, I think, did Moac. These harnesses all consisted of a wide chest-strap with a loop at each end, held up by shoulder straps; they weren't adjustable, but generally came in size increments of about two inches. You put them on like a waistcoat and tied the rope through the two loops to complete the circle; a krab might also be clipped through the loops to hold them together when not tied in, but this was definitely not for rope attachment, three-way loading on a krab being a big no-no. Around the time of the Whillans, or possibly just before, Moac also produced their Moac-Irvine Harness (manufactured by Irvine who, I think, made parachute harnesses), an adjustable harness which had a metal plate at each end, one of them cranked and with a karabiner hole, the other with a slot; you fastened it by passing the cranked hole piece through the slot in the other and attaching a screwgate krab to which the rope was clipped. Although Pete Minks waxed lyrical about the harness in an advert at the time, I doubt that it would pass muster these days due to the single karabiner link, risk of cross-loading, etc. Moac had also produced a simpler webbing belt sometime in the mid-1960s which could be worn around the waist or, with the addition of rudimentary parachute-cord shoulder straps, as a chest harness; this was also adjustable, and you either clipped or tied the rope to a large D-ring. Concern was growing at this time about the possibility of strangulation from hanging for any length of time in a chest harness, so most manufacturers had started to develop an "add-on" sit harness which couldn't be used on its own but, when added to a chest harness, turned it into a full body-harness. One-piece body harnesses also started to appear but were never popular among British climbers, except occasionally lightweight models for classic alpinism and ski-mountaineering (dangling, and awaiting rescue, in crevasses!); Troll produced a technical climbing model in the 1970s which was notably used by Pete Boardman and Joe Tasker on the West Face of Changabang, but it never made much impact on the UK market.
The second type, the "padded belt with gearloops", was pretty much confined to the UK; I can't of anything of this type made by an overseas manufacturer. I'm not sure whether the first one was made by Troll or "Tanky" Stokes, but both were similar, consisting of a stiff, wide belt with transverse webbing loops, like the belt-loops on a pair of trousers, through which the rope was threaded around the waist before tying - usually with a bowline. I think Tanky's was leather while Troll's was either nylon or polyester webbing. The transverse loops might be doubled back at the bottom to enclose a D-ring which itself could accomodate a couple of karabiners or provide one of the anchorages for a system of gear-loops. Troll brought out their Mk 2 version a bit later - but still 1960's; a bit more refined, but the same principal. Moac and Karrimor both later produced belts/harnesses of this general type, though with their models the rope was almost completely encased in a protective sleeve; canvas in Moac's case, possibly nylon in Karrimor's.
Post-Whillans, of course, proper development of the sit harness got underway, mainly by the rope-manufacturers in Europe, people like Bill Forrest, the Lowe brothers and Brian Robertson in the US, and of course Troll and Wild Country in the UK; that's all recent history, and pretty well-known.
Hope this helps.