@Masked Grizzly How long do you think your 'British Beetle' could have lasted?
Are you thinking a family of cars who's name is still going into 2019?
How does your Car company survive the 'Striking Seventies' and Thatcher?
Fedden would probably find itself wedded to the rear-engined RWD layout for its range of cars, due to it being very expensive to re-orient their production from the rear engine models to the front engine variety together with a government that simply may not have the money to help them modernize (even if it was not filled with union subversives). Even Volkswagen needed to be saved by the West German government before it began producing FWD models (albeit after acquiring NSU and DKW / Audi).
Without a similar government rescue Fedden would have probably gone bankrupt in the early/mid-1970s or struggled along until Thatcher finally put it out of its misery (similar to what
she and her government planned to do to British Leyland in OTL). The company would likely be a hotbed of strikes / industrial action / militant workforce / etc that manages to leave the rest of the British Motor Industry relatively unscathed due to essentially being a glorified make-work/ers paradise scheme, which would certainly not help its case for the company's continued survival.
What would be a grand farcical end for Fedden would be a series of OTL-inspired events including elements of the 1984-1985 UK Miners Strike, assassinations / kidnappings / years of lead / etc by a UK version of Action Directe / Red Brigades (like at Renault and Fiat plus an analogue of
the Kidnapping and Murder of Aldo Moro) supported by subversive unions seeking to turn the UK into a Cuba without the Sunshine as well as similar antics to what happened behind the scenes with DeLorean (coke, etc).
If the company does manage to survive up to the present day it would probably be at best as a low-volume aspirational/luxury carmaker akin to Porsche and Tatra by completely retreating from the mainstream Volkswagen/ZAZ segment, which would entail Fedden downscaling from its main Wolfsburg-like works town at Stoke Orchard in Gloucestershire and selling it off to another carmaker in favour of moving to a smaller plant (one it may have already owned beforehand during its post-war expansion period - especially if it never had a reputation as a hotbed of industrial action and workforce militancy).
Taking another leaf from Cuba without the Sunshine (though originally envisioned the following being for an ATL Scottish carmaker with an earlier devolved government where the West Lothian Question was resolved), perhaps either the Wilson or Callaghan governments (or an earlier Labour government) manages to temporarily save Fedden and get them to switch to FWD on the cheap via a deal with East Germany to build their own versions of the Trabant and Warburg Knight powered by four-stroke engines from either Renault / Dacia (more likely former - C-Type later possibly E-Type units enlarged to 1.6), Skoda (if under Eastern Bloc - potentially enlarged to 1.6 OHV), BMC (the A-Series was actually considered for the Warburg though following
German link has inaccurate info, Wartburgs were also planned to be shipped to Finland and retrofitted with A-Series units during early/mid-1970s prior to them leaving the UK market) and from Wartburg's own four-stroke projects (from an ATL Wartburg-focused 80-83 hp 1.6 4-cylinder OHC to a Trabant-focused 59 hp 1.2 3-cylinder OHC petrol and 34 hp 1.1 3-cylinder OHC diesel).