Find the rules on exhaust smoke content for the age of car it is and then work out whether there is anything subjective about their interpretation, then challenge the result (or take it somewhere else).
For it to fail an MOT on smoke makes me think it's burning tooooo much oil even if it has been rebuilt!
If it is borderline and you cannot argue your way into it being a pass then thicker oil might help (are you using a running in semi-synthetic or full mineral oil?).
Maybe jam the wastegate open on the turbo? This will reduce cylinder pressure which might help ... though if it smokes on acceleration you have to wonder if the oil is not coming from the turbo in the first place.
Normal run in procedure is to rev engine in a comfortable range going from wide open to shut throttle without reaching high revs or putting the engine under a lot of load (asking for lots of torque). The point here is to create lots of cylinder pressure for brief periods (run with throttle wide open) to force rings out to try to bed in to bore, then create a big vacuum (snap throttle shut with reasonable RPM) to draw oil up the bores to help lubricate the "cutting" process. So even though you cannot run it on the road, you can probably do some running in with the car on axle stands, top gear so you spin up the wheels in the air - that's still a fair bit of load on the engine and hopefully enough momentum in the drivetrain to pull the vacuum when you snap throttle shut.
Or you could build two big paddle wheels and attach to the road wheels and run in two old baths of water paddle steamer style - come on Rich, this is surely a project for you ... you could pretend it's a dyno

Seriously you could sweet talk somewhere that has a rolling road to letting you run the car in on the rolling road; provided you book it in for "engine smoke check and fix" and then you only drive it home->rolling road->MOT->home (if it still fails), you should be OK with the law.
Cheers,
Robin