Ha I remember putting winter tyres on my old car (pre-Yaris) and before leaving for Cornwall that evening, I called the insurance (RAC) to let them know, expecting a discount based on improved safety. They told me they wouldn’t cover any modifications at all and would only insure my car if they were “Volkswagen tyres”. I explained that VW didn’t make tyres and asked if they meant the stock tyres, but they insisted that the brand had to be VW.
Once that had been clarified, they still wouldn’t budge when I said that the new tyres had a better rating than the stock Pirelli ones that came with the car and told me I’d have to put them back on or my policy would be void. Cue last minute panic and cancellation then new insurer. They probs aren’t the same corporate entity, but to add insult to injury, the RACs main website which was linked to the insurance section had an article on whether winter tyres could improve premiums.