No one is in any doubt that recent years have seen major changes to that 'constitution'. The Human Rights Act alters fundamentally how rights are protected in the UK. Previously - everything was legal, except where it had been made illegal. Now rights, set out in the European Convention of Human Rights, are made part of English law - and are enforceable through the Courts. The House of Lords has been partially (but significantly) reformed; Devolution has given powers to Scotland, Wales, Northern Ireland and London. Referenda have become established and new voting systems are now in regular use.
Vernon Bogdanor describes and analyses these changes in his 2009 book "The New British Constitution". I have recently been re-reading this book. It is a useful tool both for students of British Constitutional Law - and for those seeking to improve the current political system. Details of the book are available here.