the road in central London where the official home of the UK prime minister is

The prime minister lives at 10 Downing Street. 首相住在唐宁街10号。

the British government or the British prime minister

The announcement took Washington and Paris by surprise, but Downing Street had been expecting it. 这个公告让华盛顿和巴黎方面都感到非常意外，但却是在英国政府的预料之中。