I bought a new 118i in April 2017 and after about 1,000 miles I noticed blue smoke appearing from the exhaust when starting the engine from cold.
The dealer took the car in and and returned it after 3 days saying this new engine has a fault where the rocker-box breather allows oil vapour to pass into air intake for the injection system. The oil vapour then condenses as the engine cools down and when the engine is restarted the oil is sucked into the engine and burns.
The rocker box cover was replaced, along with the spark plugs and the catalytic convertor.
However, the very next day the car was still chucking out smoke when started from cold.
This time the dealer said "it must be unburnt fumes and oil in the exhaust."
For the next few days I made a point of getting the engine really hot, but the problem still persisted.

The dealer has taken the car back in and now they think it may be an oil leak from a burst oil seal in the turbo.
They have been in discusssions with BMW and as yet the car is still with the dealer.

Video clip......
 

It does sound a bit ominous but it could well be a turbo seal.

If the oil disappears almost immediately then I don't imagine it should be too much of an issue but it if continues for a prolonged period after starting the engine then this could have an adverse effect upon the catalytic converter, so it would be advisable to make a note of this just in case it fails shortly afterwards.

Let us know how you get on with it

Cheers,  Trevor

Just got the car back from the dealer - John Clark, Tayside.
They have replaced the turbo unit completely.
They also gave me £300 in gift vouchers for my troubles.
Lat's hope they havre resolved the problem.
Watch this space!

Great result!

what are you going to spend the gift vouchers on ?  :-)

Let's hope that sorts it...keep us updated

Didn't use the car much over the weekend, but on start up today the smoke problem was back.
Going in to see them tomorrow.

Turns out it was condensation not smoke - I am getting paranoid about this car.
The original problem was blue smoke - definitely burning oil.
Everything seems OK just now.

Glad to hear it is all sorted now.

You may still get some residue from the exhaust if there is some oil lying in there and over time this will burn off.

Great result though