OTL got the structure right in the end... One or two companies is about right.
What went wrong was timing and project selection. Better choice of what to back and how with OTL's structure is probably the most reasonable way to get a better outcome... I'm going to focus on commericial since that really seems to be where the most went wrong, but obviously mistakes were made on the military side as well. TSR.2 and CVA-01 in particular could change things, but as a paying business I'd argue that British Aerospace is made or broken on commercial.
Personally I'd look to the V.1000/VC7, Trident and HS.134 projects as the main candidates for turning things around. It's tempting to talk about avoiding the comet crashes, but I end up agreeing with the sentiment that if not De Havilland (which had a record of skimping on structure anyway) something similar would have happened to someone else. The BAC One Eleven has a lot of potential as well, but I don't see it being an easy candidate for turning the industry around; otoh if British Aerospace does better overall and early opportunities for stretches, Trident commonality and CFM-56 re-engining the airframe could sell in very large numbers.
As far as the dust settling, really it comes down to Britain's role in Airbus. It' very easy to imagine the A320 being a primarily British project, with final assembly by BAC or what's left of it. Under the right circumstances British Aerospace could even go head to head with Airbus, and while I have a hard time calling the end of the consortium as we know it likely, it would be reasonable to imagine the unified British Aerospace being by far the dominant partner, up to and including Airbus amounting to BA bringing European partners into their projects.
So as an idea of what I have in my head:
-BOAC outright refused permission to buy American while British options exist,
-VC.7 enters service contemporary with 707, offers similar economics and better hot/high performance. Probably more difficult to maintain given embedded engines, but not more limited in expansion options than OTL 707 (frankly given the similarities it would not be hard to justify a TL in which the VC7 hurts the 707 enough that Douglas dominates the American market - the DC-8 has a lot more in the way of obvious advantages over the VC7 than the 707).
-Trident is produced in it's original 6 abreast DH.121 form, government having recognized that Hunting/BAC 70 seater (One-Eleven) will fill smaller roles and that a large Trident supplement VC7s in Medium-Range-Empire services, particularly to Africa. Export sales seem likely, this is an aircraft with numbers much like the 727 with somewhat earlier launch date facing a Boeing which has sold fewer 707s. Worst case scenario I can see North American sales similar to OTL's limited One-Eleven operations.
-Trans Canada Airlines is an obvious big and early customer for most of these aircraft, having (OTL) operated the Viscount and Vanguard, expressed serious interest in the VC7 and VC11 (short range VC10 variant proposed to BEA for same role as Trident, but which was eventually was dropped in favor of funding the One-Eleven). Not the largest operator, or necessarily a game changer (as demonstrated by the Vanguard) but certainly a big step to North American acceptance, and big enough to improve the picture against OTL's production numbers.
-HS.134 (twin engine, 757 like Trident variant) emerges in late 60s alongside stretched and re-engined One-Elevens. BEA purchases both as fleet backbone.
-BOAC ends sixties committing to some sort of larger than VC7/707 but smaller than 747 aircraft. I'm imagining something along the lines of a double deck VC7, much as Vickers pitched with the Super Super VC-10 double decker, or Boeing considered in the early 747 work.
At this point we run into OTL's Airbus program and the BAC/HS merger. How this shakes out is open to question, and in a fully fleshed timeline could play out a a number of ways, but none of them are likely to wipe out British Aerospace. I'm inclined to believe that the Super V-1000 gets cancelled in favor of a "European", but very much British led, four engine wide body project. OTOH if OTL's politics are anything to go by, and I don't see why they wouldn't be we might see the UK walking away from the partners and pushing the three-eleven or even saying the HS.134 is big enough for European operations into the 70s. Either way something like OTL's airbus becomes very possible and even more tenuous. In any case, the industry will be shaken up, and something is going to break. The end result will almost certainly include at least one of these major projects being a commercial flop on at least the scale of the VC10, and I have a hard time seeing the single European survivor not being British led, but this is where details matter a lot. Suffice it to say this is a TL I'm interested in writing, but there are a lot of those and I have yet to come close to actually posting any of them... Frankly if I do write it up it will probably be as part of something bigger including Britain holding some colonies, a lot of Transport America inspiration across the Atlantic and a Cold War that plays out much more multi-polar.