You need to make sure you use the right measurements when translating recipes from the US to the UK as the UK uses imperial measurements which are different from US measurements. There are also differences in cream fat content and egg sizes. Teaspoons and tablespoons are the same, so don't worry about them.
First, pint measurements, as the UK doesn't use cup measurements. The UK pint is 20% bigger than the US pint, so if you are using UK pints to measure you may be getting ratios wrong. Use Milliliters instead when translating. 1 US Cup is 237ml (I round up to 240). If you use UK pints as a measure instead of US you won't have enough baking powder in the ratio. In fact, I find UK baking powder and bicarb a bit weaker than US powders, so I increase those measurements a bit anyway.
What works for me is the first time I make a US recipe in the UK I weigh the dry ingredients and use weights every time I make the recipe after that, I can fine-tune it that way.
US light cream is between 10-30% butter fat, and heavy cream is about 36-40%. UK single cream is between 10-30% fat, whipping cream is about 36%, and double cream is 50% fat. So if you are right that US heavy cream is UK whipping cream, but mixing 2 parts UK double and 1 part single works just as well as many places don't stock whipping cream.
I doubt that your results come from the cream you are using though, the fat contents aren't that different. One thing that could be different is the flour you use. US and UK flours aren't completely the same. For my biscuits in the UK I buy 00 or purpose milled pastry flour, which is finer and better for pastry than the bog standard stuff. If you can't find it pick the flour with the lowest protein content you can find.
Hope this helps, let the forum know your results if you can.