Re: Ironic...
"maybe, Leavers just don't understand how international trade works?"
Nail on the head, right there.
It's worth pointing out that the customs duty we charge the EU will matter, as it will affect whether our food producers are able to be competitive against EU producers exporting to Britain. HMG would have to match the tariffs simply to keep that sector of the UK economy alive. This will make EU goods more expensive in the UK, which will likely mean that it just doesn't make sense importing low-margin commodity items like milk, butter, vegetables etc. On the other hand, there are items which will just increase in price, but still be worth trading as the UK doesn't produce direct equivalents - wine, cheese, beer etc (and BMWs, though that's slightly off-topic).
HP sauce probably fits in the latter category, so it'll just have a price hike to cover the import tax (the producer absorbing this costs seems unlikely). This will make the upmarket (but domestically produced) Tiptree alternative more attractive. This is what Brexit means - less choice, tariffs on some of the remaining choices, and therefore higher prices overall.