'Hawks eat over 250,000 songbirds daily'
That works out at 3.1 songbirds per hawk per day (40,100 sparrowhawk pairs, 300 goshawk pairs). According to the Hawk Conservancy, songbirds make up 90-98 % of sparrowhawk prey, so you can add roughly half a vole to that number.
Blue tits, 7 million birds, av winter population, double their numbers when the nestlings fledge to 14 million and are back to 7 million by the winter. So on blue tits alone, most the sparrowhawk population can survive without making a difference to the population of blue tits.
Of course, when you factor in chaffinches, greenfinches, great tits, house sparrows, etc, it's not that a big a deal.
Plus the sparrowhawks round here make a good meal out of wood pigeons (7.3 million birds, four young per year), which something needs to in order to keep the population stable.