The reality of prices..
First, Brits and Euro citizen are usually happy to pay more.
Then, there are a lot more consideration... (I have been there a few year ago, so, let me try to remember...)
When comparing the prices you must make sure you do not compare US price before sales tax versus the UK/Euro price with VAT. It's ~20% of the difference you can explain.
Then, you have other tax cost (like local tax office charging vat or taking a cut of your profit before shipping the rest abroad, etc). Maybe around 5%, but it really depends on your legal setup.
Then, you also a problem of harmonization or prices in the Euro+UK zone. The consumer see the final price, but VAT varies between 15% and 25% in Europe, so, you adjust your Euro price, so all customer sees the same price, but you protect your profit margin.
With the UK at the top of that, you set a price for a year, estimating roughly (with a margin) what will be the parity of the currency against the bigger Euro market (because consumers usually compare at product launch the cost, usually the current spot rate, without considering VAT etc).
Eventually, you can add other costs:
- mandatory translations (depends on countries),
- ratings,
- compliance tests (e.g. electrical).
etc
All you see as a parent company is a profit margin you'd like to make per product, so, you adjust the sale price in function of those numerous "extras".