"Core vote" refers to the group of people who consistently support a particular political party or candidate, regardless of current issues or events. They are the strong, loyal base that the party can rely on for votes.
He is not following a narrow core vote strategy, but clings to that old new Labour slogan from 1997 in which he claims to act for the many and not the few. (independent.co.uk)
Check out Andrew Hawkins» column on p8 on core votes. (totalpolitics.com)