What colour smoke?
White and makes your eyes water, unburnt diesel - probably knackered glow plugs in the engine - once the engine is warm and it clears then you'll have no issues with an MOT.
Black - Soot, over fuelling or lack of air flow (blocked filter), open the revs up to about 2 - 3 K once the engine is warm, does it fill the street with smoke? If so it'll fail the MOT visual test.
Blue - Oil, yeah that's a fail on a visual
White and clears quickly - Steam - head gasket or something similar.