Tea. Ours (except for Luzianne) is awful.
Chocolate.
Perhaps marmalade?
Different cheeses would be lovely, especially Cheshire and Stilton.
I guess it’s just the supermarkets I shop in, then. They’re not standard American fare, but I don’t find them particularly rare, either. It’s just that if I had a British friend visiting me, I’d want something that I can’t easily find here (although I’d be happy with any gift given, naturally.)
(I’m actually a little surprised that Golden Syrup is hard to find. It was fifteen or twenty years ago, but nowadays it’s shouldn’t be hard to find. Whole Foods definitely should have it.)
ETA: I should also add, the stuff they use down in Louisiana and other parts of the south is called cane syrup, but is the same thing as golden syrup. But when I talk about finding golden syrup at Whole Foods, I am referring to Lyle’s.
As an American with a Brit S.O., we regularly fill orders here for our friends. Jelly babies are a hit with kids, as are Milky Bar buttons and chocolate digestives. For the adults, it is usually decent tea (Yorkshire Gold), regional treats such as jams or (god forbid) Marmite.
If it is an older crowd, they will absolutely love ibuprofen gel. We can’t get it over here. Well, we can maybe order it online for an outrageous price, but that doesn’t mean we’ll get the good stuff. Tesco’s house brand will work just fine, thank you.
Reusable shopping bags that can’t be found locally in Green Bay will probably be a hit too. It’s fun explain “Bowden’s of Harptree” or even “Sainsbury’s” to the locals here. He gets to do the same there with his “Byerly’s” and “MPR” bags. What’s really great about the bags is that they don’t take up room in your luggage, can be useful during your trip, and you won’t miss them when you get home.
Enjoy your trip.
Snowballs.
Chocolate marshmallow delights.
I know this could be hard for some to believe, but there’s no Whole Foods in Green Bay fucking Wisconsin. I suspect indian specialty grocery stores might be a little thin on the ground as well.
Yeesh!
Those items ARE all rare - you could find them, if you knew what they were and wanted them. But they are rare, meaning, the opposite of commonplace, meaning, not things that are average or popular items for consumption in the US. The majority of Americans have never heard of them, or if they’ve heard of it (like Marmite) never tried them.
Actually, that Green Bay does not have a Whole Foods or similar does surprise me. Listen, I’m not trying to be difficult. I don’t think of Marmite and Golden Syrup as “rare.” They’re in almost all the supermarkets I regularly shop at. Obviously, your mileage varies. I guess in Green Bay, it is rare after all. Here, it’s not something I would ask a visitor from the UK to specially bring for me.
They hide the Marmite with the yeast down here, by the way. Look there if you think your grocery store doesn’t carry it.
You’ve given a long list of things that you don’t think are rare and wouldn’t ask for as a gift. What would you want someone to bring you from the UK?
Some of the more unusual-to-an-American flavors of Walker’s crisps are fun for me. (Worcester, roast chicken, marmite, prawn cocktail, lamb & mint, etc.) I agree with most of the chocolate suggestions in this thread. Jaffa cakes, too. While I’ve seen a good number of McVitie’s products here, I have not found actual Jaffa cakes (just similar products from Eastern Europe.) Also, all sorts of alcohol, especially ciders from small cideries that are not distributed in the US.
I disagree. During my last trip to Britain, I smuggled home some amazing cheeses back to the states and never regretted it. There are stunning cheeses made in the British Isles we can’t get here…
My Irish friends are big Marmite fans; I finally tried some a few weeks back. Strong, for certain, and very salty…but I liked it, on toast with butter. I’ll have it again. 
Anyway, back to the OP. I grew up in Green Bay, but haven’t lived there for a while.
Another vote for good / high-quality chocolates.
Yes, there is a lot of cheese in Wisconsin, but there isn’t necessarily a lot of variety, and a lot of British cheese types are unheard of, but may still be appreciated.
Those who make this trip more than I do: I know that U.S. Customs restricts bringing in certain types of foods – does cheese fall on that list?
(And, out of curiosity…what brings you from England to Green Bay? )
pulykamell, in the first place where I lived in the US, Christmas meant yards and yards dedicated to turrón (the English part of its label calls it nougat), polvorones de Estepa… in every supermarket. El Lobo, 1880, Delaviuda, El Almendro…
Would I expect parts of the US without a huge Spanish population to have Spanish christmas treats in the “mainstream” stores? No. Would I expect the average USanian to know the difference between turrón del duro and turrón del blando or recognize those brands? Heck no. But I was living in Miami - when it comes to finding Spanish/Hispanic stuff, that counts as cheating!
Yes, different parts of the US have different availabilities of ethnic products based on their local populations. That’s obvious. I thought Marmite and Golden Syrup had crossed that barrier into “yuppie supermarket” staples, because it’s not like there’s a huge ethnic British enclave around here. As I admitted above, apparently I am incorrect about this.
Anyhow, “rare” or not, the important point should be that Marmite and Golden Syrup rarely make a good gift, unless somebody specifically asks for them.
One and Only Wanderers, if you believe the movie Love Actually, any random British guy can walk into the first bar he comes to while visiting Wisconsin and end up spending the night with two beautiful American women. Then he can meet an even more beautiful American woman and get engaged to her. Then he can return to the U.K. with his fiance and still another beautiful woman who he can introduce to his best friend.
As I am happily married, I will have to avoid such entanglements 
OK, this one’s a no-go, and in the case of Green Bay, it might be a case of coals to Newcastle, anyway, but you can’t get bangers here. Whole Foods used to carry mediocre ones, but they don’t anymore.
Shameful story: when I first arrived in the UK and heard Slade I said “Hey, they’re doing Quiet Riot covers!” When I grew older and wiser I punched myself in the face for having uttered such blasphemy.
Usually my American friends and relatives want jaffa cakes, or maybe a good lemon curd.
This. I have just finished the ones that my mother brought over from England a couple of weeks ago. Delicious.
Any cheese lover would be delighted to get hold of some new stuff to try from England. Anything imported from overseas is expensive and just happens to be what shows up locally. Bring some yummy cheeses.
How about some Branston pickle to go with all that cheese?
And yes, you can bring cheeses into the US (but not liquid ones).