The NET price of a 335i Luxury in the UK is equivalent to $47,400, which is more than the U.S. It also includes 4 years of servicing in the U.S. and a much better warranty.
Other models:
135i Coupe
UK $41,140 net
U.S. $39,300 msrp
M3 Coupe
UK $70,012 net
U.S. $60,100 msrp
M5
UK $93,503 net
U.S. $89,900 msrp
X5 M
UK $106,586 net
U.S. $88,850 msrp
640i Gran Coupe
UK $78,576 net
U.S. $76,000 msrp
So, UK cars consistently cost more than the U.S., along with the fact that servicing for four years is included in the U.S. price and a far superior warranty. The X5 M has a price difference of nearly $20,000.
So, I hope this satisfies your request.
When I subtract the 645 GBP for road license fee, then subtract 20% for VAT on the 135i, I get a price in £25,604, or $39,322. That isn't so different from the US price. Want to bet that far more of those UK 1ers will be fleet/company cars that benefit from discounting than in the US, where the cars are bought outright? That should more than account for the $22 difference.
M5:
£73,065 - 645 (-VLF), x 0.8 (-VAT) = £57936 = $89,001. Compare to $89,900 US MSRP.
640i Gran Coupe
£61,390 - 645, x 0.8 = £48,596 = $74,653. Compare to $76,000 US MSRP.
But you've chosen some fringe players in the overall profit game for both countries. Why not use an example that is more relevant to the overall profit margins.
328i
£29,065 - VAT/VLF = £22,736 = $34,927. Compare to $34,900. Big difference? Could be, in favor of US profit margins once you account for discounted 3-Series fleet/company sales in the UK.
528i
£33,615 - VAT/VLF = £26,376 = $40,518. Compare to $46,900 US MSRP. Many of these in the UK will be used as company cars or even police vehicles. You won't find many (if any) municipalities in the US that use 5ers as police/emergency vehicles. The city councils would be skinned alive, unless they could convince residents that BMW underbid, say, Ford/GM. In which case the purchase price will be far less than what a customer actually pays.
I'm not sure that BMW AG is the one underwriting servicing/warranty costs. That is usually done through BMW NA, which is a separate entitey from BMW AG.