Happened with my Honda a few yrs ago - Northumberlina.
Car stopped dead twice while driving...(got no warning so someone could literally run into you) it would start again after about 15mins or not (driving was like Russian Roulette!! especially if you were driving towards a roundabout!) The key light was on too. I didn't drive it after the second event - my adrenaline was getting high! + didn't want to cause an accident. It wouldn't start on every occasion. My garage offered to collect it from my home & didn't charge me for this.
Initially thought to be the key battery too but no it was to do with the ignition in my case and garage replaced the whole thing- £120 I think I paid them (incl labour) but they have always been brill so I dont go elsewhere but I gather it can be an expensive job (depending). My car is a sports. Not all garages give good value. Getting the right diagnosis is the most important thing.
After it was fixed they told me when it started I would see a green key on the dash still and wait for it to go off when I turned the key or car would cut out. I did what they said and fine. Told me they had trouble getting a part - as all bought up (it is a Honda prob! that is common).
Hope this helps.