Perhaps the motoring press reference was suggested on the basis that if a major garage/ household name chain, deep down knew that they were acting or could be perceived to be acting less favourably towards a customer, then the prospect of 'the motoring press' reporting an article on the issue in question might result in a change of heart by the garage so as to minimise any potential adverse reputational damage from such an article which might otherwise be bad for business. What Car magazine showcase a 'help' section each month, for example.
If your car was bought second hand, it is possible that VW customer services will oversee to a point but will reach a point where they will take a view that they feel less able to directly intervene because you did not by the car brand new 'from [them] VW' and hence your issue is to do with the supply (or failure to do so in some cases) of goods and/ or services by the VW franchise in question and therefore any dispute is contractual between you and the given franchise. However, VW customer services representatives will also have Line Managers that complaints and disputes can be escalated to if you are not satisfied with their initial conclusions reached.
@Jags
1. Have you considered seeking legal advice (sometimes your vehicle insurance, household insurance and/ or Bank provider will provide free legal advice in cases like this. Did you pay your initial diagnosis fee via credit card because again, some credit card providers will provide a free telephone/ legal advice service)?
1A. The Citizen's Advice Bureau is also a consideration.
2. Have you considered commissioning a respected independent VW specialist review of the timeline and having the vehicle independently inspected by that person by way of second opinion on the current state of the car, actual rectification works required (& costs) and events that occurred leading up to the failure to determine whether or not that specialist can either support your argument or suggest a more cost effective alternative outcome?
3. Have you considered now escalating your grievance to Director level beyond Branch Manager/ Branch Dealer Principal level, fully articulating your grievances to such Director(s) and explaining that you have already and/ or intend to report matters to the motoring press; and/ or seek legal advice; and/ or report matters to Trading Standards & the Citizen's Advice Burea; and/ or commission an independent inspection?
The outcome now really depends on how aggrieved you feel (in hindsight, on the basis of what they told you at the time, do you feel at all that you could reasonably have done more to avoid this failure?). The outcome also depends on how dogged you are not to accept the current offer and how much time you are prepared to invest articulating your grievances to the most senior people in the correct manner/ in writing via email and not via telephone discussion as everything needs to be documented.