E30 Zone

I've recently purchased a 320i auto. I drove it home from London to Donegal (Ireland). I had to top up the oil a few times and used over 2L over the trip. The car is smokey on startup, but runs quite well. The idle is a bit lumpy when warm, but quite good. Temp guage behaves itself and it's using no coolant.

It's an April '83 car with 107,000 on the clock.
There is no service history, but seems to have been well maintained over it's long life. It was owned by the wife of a BMW mechanic from new.

Where should I start looking. I want to save the engine as the car is in very good original condition.

any obvious leaks? if there isnt then it will be burning it.

No leaks that I can see. I presume it is burning it. What should I be looking at?

I'd say piston rings

Start with the valve stem oil seals. Much cheaper than piston rings, and fits in with your smoke at start up.
Look in your mirror when you apply the power after a long downhill stretch with no throttle. Any blue smoke?