Rootes is the prime example with their having to ship engines down from Scotland to the Midlands to be machined before being sent back up, but if they had set up machining facilities at Linwood to be more self-contained is there then much difference between it and the foreign/multi-national companies?
The foreign/multi-national carmakers had the fallback option of factories on the continent in the event subversive unions in UK factories decided to hold strikes (or vice versa e.g. Ford of Germany, Opel), in fact after the UK joined the ECC many of the imports by the late-70s onwards was coming from Ford and GM via factories on the continent.
Of the UK carmakers Morris could have potentially had a factory on the continent pre-WW2, had they acquired a larger French carmaker like Cottin & Desgouttes, Rochet-Schneider or De Dion-Bouton (to potentially become their version of Simca) instead of
Léon Bollée* in OTL (where William Morris was basically manipulated into acquiring a small provincial factory that never regained its footing after WW1 as the result of the late founder's beguiling yet eccentric widow Charlotte without doing any research, since the company featured a second rate workforce and no dealership network with all the best people gone to the big carmakers and garage trade).
Later BMC had an opportunity to acquire Borgward given the alleged OTL interest BMC had, so BMC could have effectively had two factories in Europe to source production from in the event of strikes like both OTL Ford and GM. Thereby avoiding their OTL situation (especially after the formation of British Leyland) of multiple single points of failure in their production network stemming from a strike at a single plant impacting other factories / etc despite the duplication of many production facilities in the UK.
*- Apparently Madame Bollée was burdened with the factory upon the death of her husband, and when William Morris and few others visited "she fell around neck and cried on his shoulder, and every time she cried, up went the price" "Eventually he bought it..." (in Morris: The Cars and The Company by Jon Pressnell)
Out of interest was Stoke Orchard the only site discussed for the proposed plant or were other locations considered do you know? I'm not sure why but Herefordshire or the East Anglia region are ringing faint bells, although that could just as easily be a misfiring synapse what with my less than great memory.
Stoke Orchard appears to be the only proposed Wolfsburg-like site mentioned both online as well as in Bill Gunston's book Fedden - The Life of Sir Roy Fedden.
Fedden during his time at Leyland in the 1950s did suggest Leyland should have invested in building a larger commercial diesel engine for a wide range of applications as well as a new Leyland development laboratory beside the London Transport Depot at Borehamwood, only to be undermined by Stanley Markland prompting Fedden to quit though remaining on good terms with Henry Spurrier.
In Leyland's case and relevant to Triumph after the former acquired the latter, would have been to build on its links with Saab (e.g. the Saab / Triumph Slant-4), who were at the time merging with Scania to form Saab-Scania. As in retrospect it was a missed opportunity for two truck manufacturers, both outside the ECC at the time and both knowing or realizing (or should have realized in Leyland's case) that to survive they needed to become significant players in its truck and bus markets.
With the odd POD (e.g. Leyland acquiring a debt-free successfully expanded Rootes Group sans Singer, which is quickly renamed Leyland and slots below Triumph and Jaguar) it could be the case of ATL Leyland actually being in a position to acquire Saab-Scania (where Saab's reputation for over-engineered cars rubs off on the rest of Leyland), instead of Saab being acquired by General Motors.
