Opening a Commons debate on the Human Rights Bill, Mr Straw gave the strongest possible assurance to press critics that the legislation would not be used to introduce a backdoor privacy law. But the Bill - which enshrines the European Convention on Human Rights into British law, "bringing rights home" from Strasbourg to the domestic courts - will give teeth to the Press Complaints Commission's self-regulatory code of conduct.
A government source said that officials were in discussion with the commission to see whether the code could be strengthened, with the possibility of fines being built into the system of self-regulation.
The deal to change the balance of the Bill more firmly in favour of the press was struck at a meeting last Friday between Mr Straw and Lord Wakeham, the commission chairman.
Mr Straw told the House: "We have repeatedly stated our support for the freedom of the media and our opposition to a statutory privacy law."
But he recognised press concerns, and saw it as the duty of government and Parliament "to assuage those anxieties if we possibly can." To fulfil that duty, a framework of amendments to the Bill had been agreed with Lord Wakeham, a former Tory minister.
Under the European Convention on Human Rights, there were two articles of particular concern: "The Article 10 right to freedom of expression, and the Article 8 right to respect for private and family life."
The Home Secretary said it was worth pointing out that in practice, the Strasbourg-based European Court of Human Rights had extensively used the convention "to buttress and uphold the freedom of the press against efforts by the state to restrict it."
Those European judgments, would have to be taken into account by the judges in this country he said, but Mr Straw accepted that there was the need for further reassurance.
He had agreed to an amendment to the Bill, containing "an explicit provision on the face of the Bill that, in any case in which a person applies for relief or a remedy on Article 8 grounds related to respect for private life, and the granting of a remedy would raise issues concerning an Article 10 convention right, the court must have particular regard to freedom of expression."
Mr Straw said the amendments would "constitute a useful signal and reminder to the United Kingdom courts" that the balance was tilted against privacy and in favour of media freedom.
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