Wiktionary
cross the floor
vb. 1 (context UK politics of a member of a parliament English) To vote against one’s own political party in parliament. 2 (context UK informal politics of a member of a parliament English) To resign from one’s political party and join another party, resulting in moving from one’s currently assigned desk or seat in the legislative chamber to a new desk or seat physically located with the other members of one’s new party.