There was nothing fundamentally preventing the British aviation industry developing a competing airliner to the 707. Let's not forget that without the USAF tanker deal the 707 may never of gotten off the ground quite so quickly, the DC-8 too owed something to military transport origins too.
The V.1000 fits that mould perfectly, except it was a luxury for the RAF, had a weight problem that could not be curtailed sufficiently for tropical use at high gross weights. Whether that would have mattered for the transatlantic run is open to speculation. The big difference is that BOAC didn't want anything to do with it. In all the files I've read at Kew on the V.1000, commercial prospects were so dearly wanted by the MoS and everyone thought they had a potential winner to succeed the Comet but BOAC is strangely absent from the files.
BOAC often felt that it was being saddled with aircraft it didn't want, in the VC-7 and Concorde they were probably correct, but it seems rather strange that with the MoS, later MoA and other bodies like TARC that BOAC and BEA never really sat down with industry and said "build me a Stratocruiser" or "build me a 707". Often BOAC and BEA didn't know what they wanted in terms of passenger payload and economics, but they saw American mass produced airliners as cheaper and if commerical giants like TWA and PanAm were happy then it was good enough for BOAC. The US had a massive internal market and numerous large operators. Types like the 247, DC-3, DC-4 and Constellation were driven by airline demands but even by the 1940s the R&D expense meant that groups of airlines were involved, there was no chance to cater for specific needs of one, but the economic needs of 2 or 3 transcontinental airlines. Britain was different, BOAC and BEA had different markets and so getting a joint design was harder and meant that specific requirements were difficult to resist and export needs were firmly second place.
Now lets turn to exports. British industry was never known pre-war as a commercial aircraft giant. Imperial Airways were flying some very odd bespoke designs of biplane design that had no export appeal at all. The C-class flying boats were cutting edge and indeed much admired but by 1945 they were outdated technology as flying boat operations wound down across the world. Britain never had a serious competitor to the Fokker trimotors, nor even the Junkers Ju 52 and when types like the Lockheed Vega and Boeing 247 appeared even Junkers was driven to jump onto the high-speed passenger bandwagon with the Ju 60. Then the DC-2 and DC-3 appeared and by then Europe had little to compete - monoplane tri-engines were still king in France, Italy and Germany. Britain began to buy American Lockheeds and dabbled in the DH.91 and DH.95 which were good but not world-beaters. Dragon Rapides sold well and they were probably ideal for small airlines during the early 1930s but lets face it, using them until the late 50s was stretching them a little far.
So now its 1945, Europe's industry is smashed, Britain only has one major competitor, the US. It wants to fight the US in all markets and get sales in America too. In the Comet, Britannia and the Viscount are the high-tech contenders. But the fill-ins are converted bombers; Lancastrians, Yorks, Tudors, Haltons, Hermes, Viking and most of these have a lamentable tale and indeed something like the Viking or York should have been technically possible in 1939. Brabazon types are a mix of useful types, pre-war hangovers and technocratic dreams. To be fair the US had the Lockheed Constitution which like the Bristol Brabazon was a large white elephant but the Boeing Stratrocruiser had some economics in using B-29 parts and was not too large to be uneconomic. The Viscount is smash hit, it fills a niche in many world airlines including America which has stuck to the tried and tested economics of piston power. The Dart was a success and proved fairly easy to develop. The Proteus was less trouble-free and the Britannia arrived too late to make any impact and had it been 5-3 years earlier it could well of done well even in the US. The Comet story we know, had it had circular windows and never crashed it might of had more success but its hard to dream that it would have acquired quite so many sales and varied operators around the world than the Viscount managed.
Britain was so focused on the US that it often neglected to bother about its European rivals during the 1950s. European industry rapidly recovered but again still had little to compete with American airliners. Italy's early efforts in piston airliners are graceful but not commercially successful. France slowly builds up with some oddities like the Deux-Ponts. The Caravelle hit the next ideal niche, the jet-powered Viscount replacement that spurred on developments in Britain and elsewhere, limited US market penetration was gained. Boeing hit back with the 727, Britain drew up several designs but the Trident was crippled by BEA and DH lacked the faith in selling the larger version abroad. Would the Bristol 200 really have had more success in the US? That's doubtful as the 727 and DC-9 would have mopped it up as an outsider relatively easily. But France was a one-hit wonder too, the Dassault Mercure followed all the British mistakes of following one customers needs too closely. Technocrats saw SSTs as the future, so Britain and France desperate to forestall US efforts and Condorde was born. Options racked up, the Oil Crisis killed those but its open to speculation how many of those orders were genuine and the US market was tightly ringfenced (I don't 100% buy the claims that the US murdered Concorde as it was a tough market to break into anyway) - the US industry backed away quickly having tried to leapfrog Concorde but economically they were soon proven correct to do so.
Having not had a successful competitor to US airliners since 1935, Europe decided now to band together and hit the mass-transport 'Airbus' market. Airbus was formed. Britain remained too focused on beating the US and increasingly Europe. The 2-11 and 3-11 were sound designs, but hopes of a new national revival were crushed by the costs. Even had they gone ahead its hard to believe either would have been a commercial success. Lockheed's attempts to break into the market with the Tristar failed and nearly took RR with it. The DC-10 did ok but Boeing accelerated ahead, killing the MD-11 and MD-80 series and romping ahead to dominate the US and world market. Airbus had a slow start but never gained a real foothold until it had a family of airliners it could offer.
This is where Britain fell flat. It was too focused on long-distance transatlantic and Imperial routes from 1920 onwards. It never devoted the same resources to European routes where the traffic was highest and the profits to be made. American commercial dominance came from the same inter-continental routes - it bore the 247, DC-3, 727, 737. The Viscount, Caravelle, F28, 1-11 tapped into this market and won bigger slices. But Britain purely dabbled. The DC-3 replacement was left to the manufacturers to sort out and government eager to hoover up any exports that might accrue - leading to the 748/Herald spat sorted by backing whoever won the big Indian contract and while they fought Fokker cleaned up the European market with the F27. Dozens of other DC-3 replacements were stillborn. The 1-11 had begun as the Percival 107, it took Britain's only remaining independent airline BUA to launch it. BEA dabbled with the Trident and the stunted remains proved commercially useless and saddled Hawker Siddeley design teams for another decade trying to make it exportable. The 146 was stifled at birth, paused for years when it could have been flying much sooner. Again, the 146 aimed at the feederliner market and won a decent slice of the market.
The V.1000 had been a sign, the omens were clear; stop dithering with small niche markets and hit the big profitable markets. The same was true of light aircraft, US home demand created a massive industry and Cessnas, Pipers and Beechs swamped the world markets, Beagle came along 20 years too late and could never compete.
Data:
Long-Range
Britannia - 87
VC-10 - 54
Tudor - 38
Hermes - 29
Concorde - 10 (UK)
Medium Airliner
Viscount - 444
1-11 - 236
Comet - 113
Trident - 117
Vanguard - 43
Ambassador - 23
Short-Range/Feederliner/Business
Islander - 1,161
125 - 700
Dove - 544
Jetstream/31/32- 429
146/ RJ - 388
748 - 293
Shorts 360 - 165
Viking - 163
Heron - 148
Shorts 330 - 125
Jetstream 41 - 104
Trislander - 87
ATP - 64
Dart Herald - 50
Marathon - 43
Cargo
170 Frieghter - 214
Skyvan - 149
Argosy - 17 (+56 for RAF)