This is only part of what they say. They go on to say
Cat predation can be a problem where housing is next to scarce habitats such as heathland. It could potentially be most damaging to species with a restricted range (such as cirl buntings) or species dependent on a fragmented habitat (such as Dartford warblers on heathland).
Are cats causing bird declines?
Some more UK cites. This is by the RSPB PREDATION OF WILD BIRDS IN THE UK
It is conceivable that predation by superabundant and well-fed predators such as domestic cats, could lead to the decline of continental species, if only on a local or temporary basis. Baker et al. (2003) recorded a negative relationship
between numbers of wood mice and the numbers of cats visiting suburban gardens. This suggests that high levels of cat activity may deplete the numbers of otherwise common species, such as wood mice, in local areas. It is not possible directly to discern the process of hyperpredation in the data recorded here, though the occurrence of species of growing conservation concern among the prey records, such as water shrews, yellow-necked mice and harvest mice (Marsh, Poulton & Harris, 2001; Greenwood, Churchfield & Hickey, 2002; Moore, Askew & Bishop, 2003) gives additional cause for concern. Churcher & Lawton (1987) concluded that cats had a significant impact on house sparrows in the village they studied. A potential link between the frequent occurrence of sparrow predation in this and other studies and the pronounced decline in this species throughout Britain, should, therefore be considered and experimental work is called for in the light of this descriptive study.
In conclusion, this survey confirms that cats are major predators of wildlife in Britain. Further investigation of the extent and nature of predatory behaviour among domestic cats is clearly warranted by this initial work. In particular, detailed observation of cats in the field and description of the numbers of animals they kill and the proportion they retrieve are essential. Investigation of the response and attitude of cat owners living in a range of environments to the predatory behaviour of their cats would also be valuable
Also from the Mammal society Domestic Cat Predation on Wildlife
There are an estimated nine million domestic cats in theUK, and there is increasing concern about their possibleimpact on native wildlife. By no means are all catshunters, but extrapolations from prey returns by relativelysmall samples of cats (May 1988; Woods et al.2003)indicate that, nationally, they kill millions of birds eachyear. The house sparrow, whose numbers have halved in the UK since the mid 1970s, is one of the species most frequently killed by cats. However, house sparrowsare short-lived and have high reproductive rates, andwhether cats impose an additional mortality on sparrowsor simply kill similar numbers to those that would havedied anyway – for instance by taking young or weakindividuals (Møller and Erritzøe 2000) – is unclear.Populations of some other birds commonly killed by cats, for example greenfinches, have increased (Ravenand Noble 2006).
Declines of house sparrows in the countryside have been attributed to agricultural intensification (Hole et al.2002). However, there have also been spectacular declines (>90%) in several UK cities (Crick et al.2002;Summers-Smith 1999) and a high proportion of theirpopulation occurs in gardens (Bland et al.2004). In anarea of Bristol, cats killed at least 45% of the estimated post-breeding population of house sparrows annually(Bakeret al.2005). A recent study, however, has shown that nestling starvation – sometimes of whole broods –has played a major role in reducing house sparrowbreeding success in Leicester (Vincent 2005). A large-scale experimental test of whether lack of invertebratefood for chicks limits house sparrow populations is currently being run by the RSPB in London
Whether cat predation has contributed to house sparrow declines remains unclear. Nevertheless, it is prudent to adopt a precautionary approach to the impact of this non-native predator, and to design and adopt methodsthat reduce the numbers of sparrows, and other animals,killed by cats.