It might sound obvious, but do I have to buy whipping cream for whipping?
Only double cream (or whipping cream) is suitable for whipping. Take care not to over-whip though, as this can make the cream look curdled and it won't fold into anything (untreated Jersey cream is prone to this). If you have to fold cream into anything, beat it only to the 'floppy' stage. For piping it has to be slightly stiffer – beat until peaks are left when you lift the whisk (but again, don't overdo it).