The exact dose received by the NHS scanners is not public knowledge since most hospital have multiple scanners, and the dose rather depends on individual patient and scan requirements.
There are a number of NHS hospitals in Glasgow, with modern scanners. Have you spoken to your consultant or doctor regarding your concerns over the x-ray dosage, as they maybe able to refer you to a hospital with a lower dose CT (but understand the different in dosage rates is minimal)?
If you are looking to go private, I would suggest you look at Nuffield, or BMI, and request to speak with the radiographer, or get the radiographer to liaise with your doctor\consultant, as to your specific needs.
I am sure you have already done your research, but thought I should add the COMARE report which the NHS has summarised here, doesnt suggest there is a higher risk of dosage from NHS CT, compared to Private CT, and this was a very detailed study, though admits there is a lack of data. To this end I think the best approach would be to consult your doctor, or consultant, and if your concerns are not satisfied ask for confirmation on the dosage which you will be exposed to by the radiographer.
There should be an option to provide contact information, so it is sent securely. If you provide me your phone number via the 'enter contact info' box I will call you.
How did you submit your phone number, as there should have been a link to "enter contact info" just above the message box, which lets you sent the information privately to me.