Fuel light staying on and engine cutting out

[Dashley1970]

My fuel light has recently started to stay illuminated even after filling up with diesel. The gauge also drops to empty. Sometimes it goes off, particularly if driving for say half hour. However, today the car started heavily juddering in the steering then the engine cut out. Thankfully on a quiet country road. No warning lights whatsoever when the engine cut out and steering locked. When attempting to re-start the engine light illuminates and steering judders before cutting out again. Any ideas what is causing it? I was thinking the computer thinks there is no fuel and so cutting out but I've driven a few weeks without issue so assume a new problem, not fuel light problem.