I think this is something you have to try yourself as it is so subjective.
Already on this thread we've had 'Asda is the only one we use' vs 'Asda is disgusting', likewise M&S.
I don't like the Heinz versions of the 'main' products (beans and soup, we don't really buy ketchup as we're a brown sauce household, where we use the Aldi version, which is very similar to HP and about a third of the price) so I'm not interested in finding which brand is most like Heinz, but obviously this is the priority for others.
It's also good to remember that just because something is different, it doesn't mean it's less nice, or worse quality. Plus in blind taste tests, a lot of people actively prefer another brand to Heinz, that is often much cheaper.
Finally, when trying to convince DC and partners who 'could only possibly eat Heinz' perhaps frame the question as 'which do you prefer, Heinz or this other cheaper brand plus £x leftover to spend on something else' because that's what this boils down to.
Unless you have so much money that you never have to think about what you spend, it could be a noticeable benefit to cut down your beans, soup and ketchup bill by about 70% and free up more money for something else you'd like to have.