Have suffered this exact problem on my 2.2dti several times. I believe the EML light goes out after the glow plugs have completed heating, remebering that they go on heating after the engine has started say 2-3 mins on a cold day. Normally P1635 code is stored (if I have remembered this correctly!) which translates to something uniformative like " 5v ref cct#2" I have allways found one or two glow plugs duff. They should test about 1 - 3 Ohms when good, when bad 2 - 300 Ohms or dis is not unusual. ( Or use the mechanics trick of wiring them across a battery- they will glow quite a bright orangy red if good)
As an aside I have also had problems with second start of the day (when engine could be considered to be not quite stone cold) In this case glow plug indicator does NOT come on breifly, as may be expected, and car starts after cranking. Fixed it today by fitting a new battery, It was 9 years old!
I think that the odd duff glow plug can quite seriously affect overall mpg during engine warm up. I have noticed that MPG is also creeping up from 38.6 to 43.5 at current temp of -1C
PS also changed temp sensor, it wasnt that in my case.
Hope this helps, I think you are probably on the right track