How can I thicken whipping cream?
Corn starch only thickens when heated to 180 F, so it probably is not helping at all with your whipped cream.

I live in the US, so I cannot compare to whipped cream in the UK.    Whipped cream for cake fillings is often beaten almost to the breaking point to make the foam as thick as possible.  I assume you are whipping the cream sufficiently, and it still isn't getting as thick as you would like.

If that is the case, you might try stabilizing the whipped cream with gelatin.  The link is one of many I have found on a quick search, and it specifically calls for 35% cream.

This long chowhound thread also has some interesting thoughts and advise.

This ochef link also provides an interesting method of using creme fraiche.