Britain ratified the convention, which guarantees basic rights such as free speech, access to courts and protection against any discrimination, 44 years ago, but it has only been enforced by international judges in the European Court in Strasbourg.
Although their rulings are binding on the British Government, citizens can only appeal there after all British courts have been exhausted.
If it was incorporated into domestic law, judges at lower courts could give immediate rulings on alleged breaches. If the bill passes all its hurdles in the Lords, it is likely to reach the Commons later this year.
Lord Lester QC, of Herne Hill, a Liberal Democrat, introduced the bill for a Second Reading last night. He said: "Successive governments have refused to incorporate the conventions' rights into domestic law ... British judges are unable to help at home because they have no parliamentary mandate to do so."
For the Government, Baroness Blatch, Home Office Minister of State, said the Bill would strike at the heart of the principle of Parliamentary sovereignty. She said it was not for unelected judges to decide when laws should be changed.