Apple used to add 10% when they set prices in the U.K. to cover currency fluctuations, so they do not have to constantly readjust them. It is not something I monitor — because, why would I? — but I have definitely seen times that the base price for their products have been cheaper in the U.K. than in the U.S. because of this.
Notwithstanding that Canon may be fixing their prices to the Yen, but if they applied the same principle then:
$3899 at today's exchange rate = £3,088.92
+10% for fluctuations = £3,397.81
+3.7% import duty for video capable cameras = £3,523.53
+20% VAT = £4228.24
Note that import duty is not charged in the U.S. for video capable cameras (commodity code 9007100000), so the U.S. price will not have any additional charge included.
Notwithstanding that U.S. published prices are before sales tax whilst U.K. ones include VAT, you also have to accept that the net prices in the U.S. will always be cheaper than here because of the different social attitudes. A lot of what we pay for collectively through taxes, Americans instead pay for or make up individually.
Regardless of whether you prefer cheaper cameras and iPhones or free at the point of use healthcare and paid leave, until something changes on one side of the Atlantic it is impossible to make like-for-like comparisons.