US: "For Rent"
UK: "For Hire" or "To Let", depending on the usage.
Rental cars are "cars for hire", while if you want an apartment, find one that's out "to let". I found all the "to let" signs a little interesting, as it's imminently graffitable into "toilet", and the inner-eight-year-old giggles at the thought.
US: "Thrift Store"
UK: "Charity Shop"
I like this turn of phrase, as it pushes the emphasis to the good works they are doing with the money raised by selling donated goods instead on the money the shoppers are saving by buying used items. Sometimes it was hard to tell what was a charity shop. I saw several PDSA stores which fund animal hospitals and thought they were actual clinics until I looked in the shop windows.
US: "To Go"
Another emphasis change. Us American's emphasize the portable nature of our food, while the British prefer to dwell on the mechanics of the purchase. We want to "go", while they just want it out of their sight.
UK: "Rising Bollards"
There's no US version of this term that refers to posts that rise out of the roads to prevent non-authorized traffic. They're fun to watch; there is a set on the main bus line in Cambridge controlling access to a mostly pedestrian area of the city center.
US: "Open Late" - store is open past 10PM
UK: "Open Late" - store is open past 5PM
We went into a mall in Cambridge that made a big deal about its late operating hours. It closed at 8PM. It also featured a multimedia display from the local city council that had cringe-worthy parodies parodies of the MasterCard "Priceless" ads talking about penalties for moving violations and vandalism.
By the way. it's apparently a rather low-class thing in the UK to eat frozen food. The main grocery stores have a rather limited selection, making room for the chain "Iceland" which specializes in all things frozen. If you visit the Iceland site, be sure to read the slightly witty history of the store which refers to the early 2000's as "The Dark Ages", and their PowerPoint-clipart warning about management consultants.