Well, it's not nature's way to have cats killing wild birds in the UK because cats being in the UK is not part of our ecosystem and, even if we accept that they are now an introduced species, they are not controlled by the checks that nature puts in place to maintain balance between species so they cause havoc.
Normally the number of predators in an ecosystem is strictly determined by the available prey species. If there is an abundance of prey, then more young predators will survive into their first year and predator numbers will increase. That's fine, because there is enough food to support them. If the number of predators becomes higher than the population of prey animals can sustain, then food for those predators will begin to become scarce and less will survive, so the number of predators drops until it reaches a number the current prey species can sustain.
With an invasive species, they will ultimately fit into the same model because the invasive species still needs to eat too survive, but it's much more problematic because it's easy for the invasive species to do so much damage when it arrives that the population of the prey species is unable to recover: that was the case with the dodo, wiped out in less than a century of humans, dogs and rodents colonising the territory.
With cats, the problem is worse because that check that nature uses to protect against over predation is taken away due to the fact the predators are getting their necessary meals from humans, so if the prey species decline due too to many cats it has no baring in the number of cats. Cats still hunt because it's their nature to do so - we can't fault them for that. But the prey species continue to decline and with them indigenous predator species such as smaller birds of prey that rely on song birds and small rodents. If un spayed and unnuteured cats are allowed to roam freely it compounds the problem because we're not even attempting to control the number of cats we have predating the local wildlife.
I love cats personally, and I totally understand the argument that people want them to roam as they would naturally in the interests of the cat's health (perceptions of this are different in the UK than they are in the US) but our indigenous wildlife pays the price for that, and to say it's nature's way for cats to roam and reproduce freely is a long way off the reality of what is actually happening in the local ecosystem.
