Its much faster as an inpatient. A doctor has to highlight to a radiologist that the scan needs reporting. So if you are able to get a doctor to do that it should be no problems. Its difficult to say how to do that without knowing why the scan was done in the first place, but if it was something that urgent your GP would have referred you to a specialist or told you to go into hospital.
But if you are that worried just tell your GP. If your GP refuses to request the report, go to the hospital you had the scan at and tell them you want the report.
The people who are very keen and physically ask for things in hospital are usually the ones that get stuff done for them the fastest. Its just how the system works unfortunately. Those that kick up a fuss have things done for them before anyone else.