With the Rugby World Cup rumbling on, the minister put out an SOS for burly forwards. The ball, he said, was just yards from the line. With one more heave, victory would be achieved. The speaker was Tom McNally, the justice minister, as he addressed a conference on libel earlier this month.

McNally should know. He has been leading the government's bid to change English defamation law which for decades has chilled the free expression of scientists, bloggers, journalists, authors and charities the world over.

On Wednesday that impetus has received one more push: a joint committee of the Lords and Commons has reported back on the draft defamation bill, suggesting a number of important improvements. Though legislation continues to fall short in key areas, step by step parliament is removing the UK's pariah status. So bad was English law that the US Congress introduced special measures to protect Americans from courts in London, seen as dismissive of the fundamental right to freedom of expression. When the culture select committee published a report on libel, privacy and press standards in March 2010, it described the American move as a "national humiliation".

Once most MPs didn't see what the fuss was about. In November 2009, when Index on Censorship, English PEN and Sense About Science launched the Libel Reform Campaign, some suggested there wasn't much of a problem. But within four months we had persuaded the three main parties to pledge reform in their manifestos. Straight after the election Lord Lester introduced a private member's bill, adapted into government legislation by Lord McNally.

That bill, welcome as it was, proved deficient in a number of important areas. It failed to raise the bar high enough to prevent large corporations from threatening libel suits in order to stop legitimate investigation – a tactic many newspapers have suffered from.

It needed to do more to protect internet service providers from catch-all demands to take down an "offending" item, even though they may have no role in its posting and be in no position to determine whether or not the demands are simply bullying.

And it should have gone much further in setting out the public interest defence, which is the bedrock of good investigative journalism.

In its six-month review of the bill, the committee of 12 peers and MPs has dissected each area of McNally's first stab at defamation law. They describe the government's draft bill as unduly "modest" in ambition, and say that in several aspects it "should provide greater protection to freedom of expression. This is a key foundation of any free society." They suggest a higher test of "substantial harm" for claimants and a greater defence of responsible journalism and fair comment.

In a boost to academic freedom, they also recommend extending qualified privilege – greater defence – to scientific and other journals. And they follow the recent proposals of Index on Censorship for mediation to bring down the exorbitant and often ruinous costs for individuals defending themselves in libel cases brought by wealthy litigants.

It's not all good news. Despite the committee's move towards a stronger public interest defence that will take into account the resources of the publisher (a key issue for bloggers), we still believe there is further to go to ensure that the defence is robust and accessible. And some of the provisions for web forums and social media, particularly concerning anonymous comments, may be problematic.

McNally and his boss, justice secretary Ken Clarke (who seems curiously unengaged in this crucial issue), are expected to respond quickly to the report. We hope they will take the criticisms on board and incorporate the proposals that would beef up the bill. Our libel reform campaign will continue to lobby for change.

The danger to reform is likely to come from another direction. Unwittingly, the Leveson phone-hacking inquiry could do more harm than any of the avaricious law firms desperate to maintain the profits they make from defending oligarchs and sheikhs.

Lord Justice Leveson's inquiry into just about every aspect of press practice could give ministers the impression that they might as well wait for his conclusions next autumn before doing anything about libel. This would be a terrible mistake – and one the judge himself is keen to avoid. He has made clear, time and again, that he is not looking at the libel law.

With consensus achieved among the parties, and among most (if not all) mainstream legal, media and academic figures, there is now only potential inertia and misunderstanding in the way of a short, clear bill being published straight after next May's Queen's speech. Thanks to the committee's strong scrutinising work, the bill should receive speedy passage through both chambers and make it on to the statute book by next autumn.

McNally needs the impetus of Nick Clegg and David Cameron to push him and the ball over the line. A sorry chapter in English legal history will then be over. A government in desperate search of good news and solid achievements is staring one in the face.

• This article was amended on 19 October 2011 to add Sense About Science to the lead organisations behind the libel initiative