2001 BMW 320 Smoking Exhaust & Burning Oil

Hi there. I recently bought a bmw 320 convertible and noticed that there was white/bluey smoke coming out the exhaust. I took it to my mechanics and after consulting a BMW technician it was found that it needed a new cyclone unit (as it was blocked?) I had previously the week before had a new water pump and alternator belt fitted also. However, the car is significantly still burning oil and smoke is still coming out the exhaust. I noticed it's only mainly at low revs when pulling away at lights or when I put my foot down strongly whilst changing gear. I am at loss as to what is wrong with it? I wondered whether it was the headgasket but it does not over heat. If I want to go on a long journey it tends to use about 3-4 litres of oil on about a 5 hour trip which is not only excessive but also rather expensive too. Would you have any idea of what it could be? Many Thanks