One thing at a time...
White smoke and head gasket:
Head gaskets rarely go on Omegas, and even then usually only if the engine overheated for a prolonged period. So if your Omega does indeed suffer from blown Head Gasket, it would be the odd one out....
Mechanics have ways of getting rid on annoying customers (no offence meant, it is just that for some mechanics
all customer are annoying...), and quote either 'new ECU needed' or 'Head Gasket gone' hoping that you will find the repair too expensive and leave them in peace... far more sensible (for them) than spending hours diagnosing the fault down to a £30 component.
White smoke when the car is cold does not mean much, usually it is just water vapour and quite normal. It can continue up to when the engine reaches normal running temperatures (80-90 degrees).
Constant white smoke usually means valve stem problems, this is not good but not a show-stopper so the car can be driven until the problem is fixed.
What the garage was probably trying to say is that the white smoke is coolant that finds its way into the combustion chamber through a blown head gasket. But if this was the case, then you should also experience a significant coolant lose. Do you have to top up the header tank frequently? If you do not, then the white smoke has probably nothing to do with the head gasket.
EML light:
I am no expert on LPG, what but I heard from others here is that EML light does come on if the car has been converted to LPG, and this is not a problem as such. Hopefully someone else will be able to confirm
Fault diagnosis:
On the Omega, like most other modern cars, it is essential that the the engine fault codes are read. The codes will will tell you what is wrong with the engine (or at least what the ECU thinks is wrong with the engine). This is paramount before any remedial action is taken. If the garage read the codes, then post them here and you will get some advice as to how to proceed... alternatively find someone with a code reader and read the engine fault codes before doing anything else.
Hope this helps.
PS - reading your post again, it is quite possible that both the EML light coming on and the white smoke are quite normal and nothing to worry about... it is bad mechanics that give Omegas a bad name.
