My 2015 Fiat 500X 1.248 turbo diesel has developed hesitation whilst driving and is chucking out clouds of blue smoke from the exhaust above 50 mph. Having to top up oil daily and engine will carry on running with ignition switches off. Garage says there are no error codes coming up, any and all ideas welcome. Thanks

Sounds pretty serious. I'd say from the running on issue that it was diesel in the oil due to switching off during dpf regeneration, but that causes the oil level to rise, not fall.
I'd suggest trying a more competent garage - just plugging in diagnostic equipment isn't really investigating the problem.

If you are losing a significant ammount of oil to the point you have to top it up daily
You must have a leak someplace
My guess would be the turbo
Can you take a pipe off the turbo that goes to the inlet I'm betting it's full of oil

TrevC said:

Sounds pretty serious. I'd say from the running on issue that it was diesel in the oil due to switching off during dpf regeneration, but that causes the oil level to rise, not fall.
I'd suggest trying a more competent garage - just plugging in diagnostic equipment isn't really investigating the problem.

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Exactly so, a lazy garage. If the computer says No Fault Found but the car is spewing out blue smoke it's time for them to go Old School and work it out without a computer.

Sounds very much like the turbo as said, easily to see if the turbo is accessible.