In the House of Lords there is a committee composed of 12 peers whose task is to "to examine the constitutional implications of all public bills coming before the House; and to keep under review the operation of the constitution."
Its membership includes the Chair, Lord Goodlad - an experienced former MP who was, amongst other things, Government Chief Whip, and then High Commissioner to Australia; Viscount Bledisloe - a QC (leading lawyer); Lord Morris of Aberavon - a long serving Labour MP who was also a recorder of the Crown Court and Attorney General; Lord Norton of Louth - Professor at Hull University and world renowed expert on legislatures; and Lord Woolf, a former Master of the Rolls then Lord Chief Justice. A formidable committee!
As its terms of reference suggest, it produces reports on individual bills as well as on key issues. Its reports can be accessed at http://www.parliament.uk/parliamentary_committees/lords_constitution_committee/lords_constitution_committee_reports_and_publications.cfm