UK Ketchup and Mayo
Years ago, I switched my mayo from Hellman's to Heinz, because the bottle design meant there was less transfer loss.
How the tables turn: I'm back on Hellman's for mayo, and they do a well reviewed ketchup too now.
(Hellman's is Unilever, a UK based company. Although they're apparently being shits to Ben and Jerry now...)
I switched to Heinz because it is much nicer than Hellman's, and still is. Trying to find another alternative.
If you want a UK ketchup, generally stick to the supermarket own brands. Several are manufactured by Greencore, which is a UK catering company. Most are going to be from similar smaller non-brand manufacturers.
Of the brands, both Heinz and Daddies are owned by the same US company. Hellman's as you say it's Unilever, so technically British. Tiptree and Stokes, upmarket brands, are both UK. I can't think of any other brands that are readily available, other than European brands in the world food sections.
Unilever are on my no-go list because they still do business with Russia.
The 'Sauce Shop' ketchup is delicious -Nottingham based.