The Adullamite Republicans were part of the 2000 coalition that continued Whig control of Parliament. They are in favor of complete independence from the Federated Kingdoms.
"Adullamite" comes from 1 Samuel 22:1-2: 022:001 David therefore departed thence, and escaped to the cave Adullam: and when his brethren and all his father's house heard it, they went down thither to him.
022:002 And every one that was in distress, and every one that was in debt, and every one that was discontented, gathered themselves unto him; and he became a captain over them: and there were with him about four hundred men. *Here* it also referred to a group of English politicians who opposed extension of the voting franchinse in 1866. It is sometimes used to indicate someone who opposes a current leader and/or someone of extremely conservative views.