She was driving an Austin Mini, and had to open and then close the door to get in and drive away. That alone should have cleared out a significant amount of any concentrated oxygen that had built up inside the car. And cars are nowhere near airtight to begin with, so that should limited the extent of the build-up.
Her father is quoted in the Daily Mail article saying “It was her day off, and she was making her way home to do her mother’s hair, so she had her equipment bag with her and would have been carrying hydrogen peroxide in a small amount.” And she was a “mobile hairstylist”, so it doesn’t sound like she was operating a large scale hair-styling business, involving purchase of large containers of concentrated hydrogen peroxide.
Well, the unknown element to me is this concentrated 30% hairdresser and nuclear reactor-only grade H202.
Normally, H202 of any concentration decomposes fairly gradually, but my Merck index says that impurities, especially metals, can cause much more rapid decomposition. Get some heat into closed car, spill some on the carpeting with some of that glitter in there that gets everywhere and I’m thinkin’ BLAMMO. All elements present!