I think it's naive to think the only way to assure you're picking a good breeder is to focus on KC clubs and those you meet at crufts. Absolutely a good place to start but just like with profit, once you include competition you're far from guaranteed welfare. Many people, myself included, really don't rate the kennel club and some of what it has stood for, particularly in the past. When I was younger people just looked in their local paper for available litters!
I have two KC registered dogs because the breeders I chose decided to register them, I would still have chosen these dogs even if they had not been. Both my dogs came from families who bred their family pet to produce their next pet and one even advertised on gumtree 😱😱. I met the breeder, met the mum (and on once occasion the dad), visited a few times, answered all their questions (even some gumtree villains care where their pups go believe it or not) checked all necessary boxes were ticked and have now got two awesome, happy dogs. I remain in touch with both breeders and even with some of the owners of the other litter mates. I met other breeders that I walked away from including one or two from the breed club. I wanted a breeder who cared about her dog and it's pups, not about the money, not about whether I would show the pup, not about whether it perfectly matched the KC dictated breed standard. And that's what I got.......on gumtree.
But what makes a reputable breeder is a debate that is never really settled.
OP I'd keep your options open. Research your breeds a bit more (if pedigree is the route you want to go down), contact various breeders (breed club is a good start but I found it largely unhelpful. Many didn't even acknowledge my attempts to contact them, I'm sure they would had they had puppies to sell). If you decide to look on gumtree be VERY selective and don't admit it on mumsnet While I know there are perfectly good breeders there, there are also a lot who are not. As long as you make sure you meet the breeder, mum with pups and any other resident dogs, all health checks and necessary documentation/chipping/immunisation etc is all being done. Trust your gut, if anything seems not right walk away. A breeder who shows little interest in you and what the puppy will be coming to without asking any questions is one to stay away from.
I hope you find the perfect pup for your family 😊