Engine momentarily stalls and restarts randomly

Hello everyone, I have a diesel (1.4 HDi) on 213,000 kms.
The engine of the car started randomly shutting off and restarting instantaneously while on the run. My observation is that it becomes more frequent when the air gets colder (or when the climate changes in general), or when I buy a bit cheaper diesel two to three times in a row. It has been an issue for almost two years now, finally today the engine ceased responding to gas for a brief time and later simply quit running (for good, instead of usual momentary shut-off and rerunning). I was not able to start the engine for about thirty seconds. When I was going to call for a tow truck, it started after my final attempt.
A mechanic told me it may be related to a diesel pressure sensor fault. What do you say, and is it something I can fix myself?