I30 1.4 se 5dr petrol Feb 2009 58000 miles

As I came to a stop at a roundabout my car cut out. I restarted and continued and when I braked and came to a stop at the next junction the cut out again. No noises. Car had ran smoothly. No judder or engine noise or anything to suggest a problem. However, I couldn't restart and it's now at a garage.

When I tried to start it the starter motor operated but no turnover whatsoever. The garage said their preliminary inspection is that the timing chain (isn't it a belt?) is very loose and timing chain needs setup. They said they need to check if valves and engine is ok and best case is £600 or so (not sure if this includes local recovery to garage).

Not sure if this all adds up from a silent cut out . Any advice?

Thanks.