Sorry Bob, but that's not the case. If the fire started by accident (or arson), and the owner of the other vehicle was not directly responsible (ie they didn't light the fire themselves), your insurance will pay out, with no chance of recovery from the other person.
This is an established case law (Musgrove vs Pandelis).
The basics behind this is that as it wasn't driver error, or down to poor maintenance, then the owner of the vehicle can have no power over the incident, and therefore their insurers are not liable.
It's very much the same if your vehicle is hit by a stolen car - if the driver is unidentified, the insurer of that vehicle isn't liable under the Road Traffic Act.
That said, it depends who insures the car that caught fire (there are some real idiots working in some companies). We wouldn't even consider the case where I work