The Merkin condiments do pretty well.
Heinz is an established name.
Therefore Heinz sauces sell well. As well as Ketchup, a Brit staple is their Salad Cream (bleurgh! bane of my childhood!) I understand it's pretty much non-existent in America, but the iconic bottle graces many an afternoon tea over here.
I like the Heinz BBQ sauce, but Lea & Perrins (Worcester Sauce people) do a great range of shake-on sauces - for cooking - and squeeze-on sauces as well.
Hellman's Mayonnaise is also a standard.
Like many brands I actually assumed it was British (see below *) for a long time.
Tabasco.
There are now a lot of hot pepper sauces -
Reggae Reggae Sauce is climbing the charts - but this is considered original and best. Especially as there are four different flavours. Yeah - I bet you have 20...
Mustard, I'm afraid you don't figure.
There may be some people who buy "American Style Mustard" and that's probably what's dispensed in cinemas when you buy a hot dog. But in general in this country we eat Colman's. It comes from Norfolk and the distinctive colour and shape of the packaging means MUSTARD with a capital OW. What's the good of it if it doesn't sing in your sinuses?
We also eat French mustard, especially Dijon.
Colman's also sell quintissential accompaniments for all Sunday roasts; apple sauce for pork, bread sauce for turkey (that's a packet mix - we never have that) mint for lamb. When possible we buy local jars from the local butcher. We do buy Ocean Spray cranberry for turkey though, cranberry not really being a viable crop here. Or at least not a cheap one.
Oh and horseradish for beef. My favourite.
I add it to mackerel as well, and like the strong stuff.
No particular maker - I buy supermarket own. But in its absence I have a tube of wasabi.
You would recognise many condiments if you came here (please do! I'm always asking y'all!) but perhaps used in different ways.
We're not as foreign as Continental Europe, with their beers in vending machines, and mayo on fries. But we might appear exotic with our brown sauce on bacon and our mint on peas.
* Our first morning in New York. We went into a diner for breakfast. It was a little off the beaten track, but of course I can't claim it was completely authentic (although the waitress did exclaim that we were English). I was amazed for a second that there was Heinz Ketchup and Tabasco on the table. I then laughed at myself to the Evil Ex. He didn't get it, and still didn't when I explained it. Then again, he also thought Kelloggs Cornflakes were British. Blame the English cafes on the Spanish Costas, which reassure people everying they serve is the same as at home - you've guessed it, Heinz, Kelloggs etc.