The examination of a British Bill of Rights has made it through the Coalition negotiation process (pdf file) but it does seem to have been diluted somewhat in the process:
"We will establish a Commission to investigate the creation of a British Bill of Rights that incorporates and builds on all our obligations under the European Convention on Human Rights, ensures that these rights continue to be enshrined in British law, and protects and extends British liberties. We will seek to promote a better understanding of the true scope of these obligations and liberties."
However, Fraser Nelson points out how a British Bill of Rights would not solve the perceived problems that the inclusion of the European Convention of Human Rights in law by the Human Rights Act caused. A British Bill does not end the jurisdiction of the ECHR and European Court (nor its influence on the rulings of the European Courts of Justice and thus European Union Law).
The origins of the ECHR is from a firmly British perspective but the role the Court now exercises was not what was envisaged when it was established. This leaves the UK with two options beyond developing its alternative - ignore rulings in the expectation that expulsion mechanism would be highly unlikely to be enforced or withdraw from the jurisdiction of the ECHR. The latter is seen as an unacceptable option for various political reasons particularly as any rejection will be being presented as being anti-human rights and utilised by the nations that are genuinely anti-rights. However, without such a shock to the system and challenege to groupthink, how else will the runaway train that is the human rights industry be curtailed?
On the full and thorough exposition of this argument I'd recommend Dominic Raab's book, The Assault on Liberty: What went wrong with Rights.