I am also looking around for travel insurance but this underwriting issue confuses me a little.
It seems that AXA underwrites quite a few insurance policies - actually both Amex and M&S. So does that mean a cancellation will not be covered with any company underwritten by AXA?
Niether American Express nor Marks & Spencer are insurance companies - they are just lending their brand value to flog insurance written by other people (AXA in this case). I wouldn't worry too much about who the underwriter is though because different policies from the same underwriter will often have different terms. For example Royal Bank of Scotland underwrite Coutts Travel Insurance (very lenient terms) and AA Travel Insurance (quite strict terms).