Bills currently before Parliament:
The bills currently before Parliament can be categorised into public bills; private member's bills and private bills. Public Bills of particular constitutional importance are the Fixed Term Parliaments Bill and the Parliamentary Voting and Constituencies Bill . There is good reason to be concerned about these - see the comments about the Fixed Term Parliaments Bill on Head of Legal and Of Interest to Lawyers. Private Members Bills are those raised by individual members of either the Commons or the Lords. Only a few of these Bills ever get to become law since the government's legislative programme usually dominates. For example see the Defamation Bill introduced by Lord Lester of Herne Hill QC and the Anonymity (Arrested Persons) Bill. Private Bills are a third category. These are bills promoted by some person or body outside parliament e.g. The Leeds City Council Bill. They are very expensive to promote and follow a particular route through parliament - see Private Bills Factsheet August 2010.
Occasionally a bill appears which has both public and private effect. This is referred to as a Hybrid Bill.
For completeness it should be added that Parliament also enacts "Measures" for the Church of England - see. for example, here.