Crossing the floor has come to mean permanently changing political party. The term comes from the fact that, traditionally, Members of Parliament from opposing parties sit on opposite sides of the Chamber. Therefore a Member that changes party usually has to cross the floor of the House to sit on the other side of the Chamber. The term is used to signify the changing of allegiance.
Despite representing a different Party, the MP remains the elected MP for their area until the next general election, when the constituents have the opportunity to keep them in or vote them out.
Further information on this subject can be found from the following links.
Alphabetical list of Members of the House of Commons
Alphabetical list of Members of the House of Lords