Since the autumn of 2016 NatCen has polled the same panel of voters, who（主语）like the country as a whole were divided （谓语动词）in the referendum by 52％ to 48% in favour of Leave.

who 指“选民”。like 是介词“像”。介词短语as a whole 作定语修饰 the country。like the country as a whole，“就像整个国家那样”。介词短语作方式状语，修饰后面的谓语动词。

定语从句主干部分：who were divided。