My 147 did the same thing on Saturday afternoon, after all the local garages had gone home for the day of course.
Cut out at a roundabout. Boosted and restarted by a local recovery guy on behalf of the AA & then it cut out again 1 mile down the road so the car was piggy backed home.
Diagnosed this morning by second AA man as Crank Sensor fault (don't ask why the first guy couldn't do the same thing on Saturday) so I've bought one from Shop4parts and will get it fitted later this week once it arrives.
It starts and runs until the sensor gets hot and cuts out. This is why it will start again after a sufficient cooling period, assuming you don't run down the battery trying to start her, like I did, twice.
The light on the dash stays on until the fault clears (the handbook says that the fault code is retained).
BTW I'm still waiting for my local main dealer to call back with a price. Only 11.5 hours and counting since I first called them.
So much for improved service levels. I rang 4 times and still couldn't get a quote. On the second attempt they suggested that the AA diagnosis was wrong but once convinced still couldn't confirm a price. Very disappointing.
By way of comparison, the two indies I use (Allitalia and PJ Motors) both quoted prices over the phone. £120 & £110 fitted. The part cost me £31 incl delivery from Shop4parts and I expect another £40 or so on top for the labour for whoever I get to fit it.