No - absolutely no US impact, unless you get some really fringe edge case (e.g. you buy a classic car that appreciates in value and you've got a capital gain when you sell it). A standard depreciating car with a standard loan has no impact on US (or UK) taxes.
There could be an edge case similar to a mortgage, where exchange rates could cause a phantom gain - but a car loan is too small for that to matter unless you had a huge loan and/or really drastic changes in exchange rates. And it'd only matter if you sold the car before paying off the loan, so there was a lump sum "gain" - pay it off over time and there's no chance.