I bet a direct flight from Charlotte to LHR costs about $700 more than a direct flight from Charlotte to Eugene.
I can do Delta from my home in Columbia, SC to Heathrow for $974 vs. CLT to Eugene for $580. United is about $50-$75 cheaper from Charlotte to Eugene.
There's a great direct flight from CLT to Gatwick that runs $1,062 in September. Delta from CLT-LHR is about the same price, for some reason that's a rare case where Charlotte is a more expensive departure point than Columbia (usually quite the opposite).
Columbia to Manchester is a bit more expensive, about $1,100 or a bit more. Manchester to Ganton is very similar time+distance as Eugene to Bandon.
The rental car cost comparison is roughly a wash except for the more expensive fuel in England (+$50 or so). Flight costs run about $400-$500 more for transatlantic, not quite $700 but still a significant difference. Everything else about the England trip is either much less expensive (if you're talking London and the south) or much, much less expensive (Manchester and the north). I don't have terrible jet lag from either a 3-hour change or a 5-hour change but it's a minor nuisance in either case.
The real bargain is if your wish for UK golf happens to be somewhere that's not among the 20 or so courses with prime-season-Bandon-like green fees. The Muirfields and Old Courses and Royal St. George's (Open rota venues) plus some of the premium clubs in the stockbroker have roughly double the green fees of fine courses like Ganton or Royal Cinque Ports. Even at $1.60 to the pound the courses which charge around 100 quid for a round or a day ticket remain relative "bargains" compared to Bandon, Pebble, Kohler, Kiawah and the like. Plus the age-old observation that you can't even easily access the equivalent private clubs in the USA (I'd put a club like Shinnecock or Olympic Club in the same quality class with Ganton, for instance).
But that's not to downplay the hassle factor of international travel. Passports, currency exchange, cell phone issues, people who talk funny and call you "Love" or "Dear" (I'm joking there, I actually love being called "Dear" by the occasional northern grocery clerk) and the sheer distance of travel make it a much more tiring and worrisome undertaking. And in today's world, frankly it's reassuring to know if worse comes to worst I could always (eventually) drive or walk home from Oregon if the planes aren't flying. But from my neck of the woods, for really affordable and convenient vacation travel I'd need to stick to the opposite half of the country and not play at one of the big-name resorts. Which in the end might be what I end up doing after all. I know some things can't be accounted for in dollars, unfortunately my bank balance is not one of those things.