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.