I don’t have any single item in my home that would be particularly valuable in medieval Europe, but I have a number of small-ish items that could help me establish myself tolerably well:
As many have mentioned, a vast array of textiles and sewing implements that would be luxurious by the standards of the time - Cards of sewing needles, a bolt of good upholstery fabric, several sets of curtains (brocades, sheers, even simple cotton/poly curtains - the ones in my girls’ bedroom and playroom are rich purple, pink, and blue, and would be rather valuable based on the color alone, if I understand medieval dye technology correctly.) Also, gobs and gobs of sheets - the high thread count cottons would certainly qualify as a luxury good at the time, and be suitable for very high-end undergarments for a noble. Even the cheaper sheets would be novel, in that they are relatively wrinkle-free and sturdy, and many have patterns. Plus, the handful of silk scarves I own, and maybe a couple of my formal dresses would be valuable for their material (brocade, velvet, satin.)
My ice cream churn has a hand crank. Ice cream wasn’t really introduced to most of Europe by that time, but all of the ingredients were quite available, as was ice and salt. I could be Ice Cream Maker to the King, with plenty of kitchen boys to turn the crank!
As mentioned by others - spices. I don’t have enough to make myself rich, by any stretch of the imagination, but enough to trade for some basic subsistence items to help establish myself. (Although I might have to keep my vanilla and cocoa to myself, and well-guarded, if I’m gonna be the official Ben & Jerry to the King! No way to replenish that supply for a couple of centuries past the time period we’re discussing. Ditto for my supply of “exotic” dried fruits - pineapple and cranberries and coconut and such. If I were planning ahead for this adventure, and the rules of this thought experiment allows it, I’d go buy a crapton more vanilla, cocoa, etc. I wouldn’t really worry about cane sugar, though, since adequate substitutes existed then.)
Kitchen knives and various household knives - I have good kitchen knives. Those are expensive now, and the quality would have been recognizable then, too. I’d likely keep at least a couple for myself (chef’s knife, paring knife, good pocket knife,) though, if this is a situation where I’m required to remain in that time. Really good pocket knives would have been valuable, I think, although I might have to “invent” the pocket! (I know, people typically used pouches, probably because of the high cost of textiles, if I’m guessing - no need to replicate the same thing on each garment.)
I’d definitely take sturdy shoes, but those would be for personal use. Everything I think I know about medieval shoe technology makes me think I wouldn’t find most very comfortable or practical.
Hosiery - imagine a 14th century lady’s reaction to nylon panty hose or tights!
Medical supplies - Thanks to my husband’s recent medical history, I have a ton of stuff in my Zombie Apocalypse medical bag. Broad-spectrum antibiotics, powerful anti-inflammatories, opioid pain medicines, etc. Plus common “modern miracles,” like aspirin and antibiotic ointment. Hell, I have a first aid kit that’s suitable for minor surgery! If the Ice Cream Maker to the King thing didn’t work out, I could set myself up as a doctor, at least until my supplies ran out. I’d take my first aid books, too, but those would also be for personal use. And if time allowed, I’d get every vaccination available to me in modern times, including (especially) smallpox, if at all possible. And I’d get my stepbrother to write me as many prescriptions as possible for basic antibiotics and get them filled ASAP. Most of those would be reserved for myself, but for the right price, I might save a wealthy nobleman’s son from an ear infection or something…
There are also about a dozen pairs of reading glasses floating around the house - those would have been the newest technology in Europe at the time, and certainly worth a bit to the right buyer.
I also have a bit of silver - trays and bowls and pitchers and flatware. No argument that those would be worth carrying.
And, thanks to having kids in school, I have a metric buttload of notebook paper, ballpoint pens, pencils, crayons, felt tip pens, etc. Sell that stuff to the local monastery, along with a couple of books I have on hand - nothing in modern English, but a bound, printed copy of Galen or the Koran or the Septuagint would be terrifically valuable, and out of the price range of anyone except the wealthiest noble or monastery. I also love the look of maps, and I think I have a reproduction of a couple of 18th century maps of Europe, Africa, and Asia. They aren’t accurate, but they’re better than four centuries earlier, and would be worth a few pennies to a military leader.
Thanks to our recent home remodel, I also have some quite portable and common items from today that would be expensive then - nails and hinges and screws, good chisels and hammers, etc.
Jewelry, of course. I don’t have any major stones, but fine gold or silver chains, semi-precious stones, and even costume jewelry would find a market, if only for the novelty of the workmanship.
Seeds: I have several packets of them - tomatoes or maize would be quite the novelty, and watermelons had only just been introduced to Europe by the early 14th century, although I assume they might have to be cultivated in a greenhouse in England. With enough lead time, that 10-pound bag of potatoes in the pantry might become enough seed to help alleviate the oncoming famine, or maybe just keep myself or my village fed. That bag of green peanuts I have for boiling might also serve the same purpose, but cultivation would probably have been very difficult in England - Spain seems more likely to have the right soil and climate conditions. Considering their nutritional value and the use of the tops to feed livestock, though, they’d certainly help during famine conditions.
Even something as cheap and simple today as the dozens of drinking glasses and glass kitchen implements in my cabinets would be very rare and valuable in 1310 England, as would my porcelain dishes.
Is there a weight limit on what we can bring? I keep thinking of more and more things…