Sorry to hear this Colin, I can understand your frustration and disappointment. Unfortunately I think you will be luckily to get Lexus to help you out given that they have already provided an additional 4 year warranty to the car, essentially as a 'good will' gesture. A line has to be drawn somewhere, even if it was 4 weeks over 7 years they would be unlikely to help.
Sale of goods act gives you a case against the dealership rather than the manufacturer, depending on when you purchased the vehicle you could have some luck - if it was purchased new then after 7 years I don't think it would be unreasonable to expect repairs to a vehicle, but if you purchased it 12 to 18 months ago and now face a repair bill that is a significant percentage of the vehicle's value then you are in better shape to have at least some compensation.