MPs and the Lords need not always belong to any political party. MPs can sit as independent candidates and Lords can sit as Crossbenchers or Independents.
Lords and Bishops
The Anglican Archbishops of Canterbury and York, the Bishops of Durham, London and Winchester and the 21 other senior diocesan bishops of the Church of England sit in the House of Lords.
Crossing the Floor
The Members of the House of Commons or the House of Lords can change their political party any time. This is known as “Crossing the Floor”. A member who changes the political party, usually has to cross the floor of the house and sit on the other side of the House.