Traditional ways of thickening cream are culturing, or making clotted cream by heating raw cream, then leaving to sit. There do seem to be some ways of whipping raw cream, but it does take some preparation.
1. Skim well – Pour your cream into a wide mouthed bowl or container, and leave for 24 hours or so. You will then be able to skim full cream off the top and be sure you don’t have remaining milk in it.
2. Age it – Older cream whips better than fresh cream, so the skimming stage will allow that to happen. But there is a fine line here, if you leave it too long, it will sour, and that may not be suitable for your needs.
3. Chill it well – It may also help to chill your bowl and beaters. Cream turns to butter faster when warm.
4. Beat it fast – Use the fastest speed on your beaters. (But be careful starting up, so you don’t spray cream all over the kitchen. A bigger than usual bowl helps too.)
5. Additives last – If you want to add flavourings (eg vanilla essence) or sweeteners (eg stevia, maple syrup) add them AFTER the cream has thickened enough.
I can’t guarantee this will always work, but will increase your chances.