House Sparrows rely on humean habbitation and stay loyal to a particular nest site, so if Sparrowhawks nest nearby I would say Sparrows are unlikely to re-locate and thus become a sitting target.
In the pressence of Sparrowhawks it has been shown that Sparrows and other songbirds maintain a lower bodymass percentage in order to evade capture. So if their diet is not of high quality(eg large quantities of bread) there is great risk of weakness starvation.
BTO, Leiscter, Oxford and other studies have associated large densities of Sparrows with high densities of bushes, especialy native. I believe that this as many others do is because they provide protection and an invertibrate food source. So greening up a park several hundred metres away wont matter if the imediate area around the nest site is devoid of bushes.
Leicster study showed that summer broods that relied on vegetable food mainly failed. The Leicster study was judged by Summersmith who is the most well known and respected Sparrow expert in the world, I doubt that he has political ties with the RSPB.
Sparrows in the countryside have been shown to be slightly larger than their city dwelling counterparts suggesting a poorer diet (invertibrates prehaps).
Sparrows have been shown to rarely travel more than 1.5km from their nest site, so interaction with other viable colonies may be difficult. This could cause an interbreeding problem that may lead to genetic weakness.
Many people say that predators only take geneticaly weaker birds or a 'Doomed Surplus', I have to say that with the amount of predators a Sparrow has, they would have to be a genetic superstar to survive, its a wonder there are any sparrows at all.
Maybe cover was not necessary when hawks were not around but now it is. Either way it is the disappearance of woody vegetation in close proximity to properties that would be the major cause for the decline.
And let us not forget about nest sites. It cannot be denied that thousands of people have inadvertantly sparrowproofed their homes, and don't say they can go and nest in bushes, they have all been ripped out.
