In the UK, private calcium score scans generally cost between £250 and £650, depending on the clinic and whether a cardiologist report is included. Places in the regions tend to be at the lower end with London and the larger hospital groups slightly higher.
You can often self refer and get it done in a week or two. No contrast dye needed and the scan itself is fast. The results are usually returned within a couple of days.
There is an NHS route but the waiting lists can be long unless you have clear symptoms or risk factors, so most people go private if they want it for peace of mind.