A rare round of applause greeted the news that British computer hacker Gary McKinnon will not stand trial in the US.

Clapping is normally frowned upon in parliament but a few MPs on both sides of the Commons were unable to contain themselves as Theresa May announced she would put a final block on American prosecutors’ efforts to extradite the 46-year-old.

The home secretary also gave her long-awaited response to a legal review of the US-UK extradition treaty and announced a number of changes.

Campaign groups and politicians from all parties have claimed the current arrangements are unfair and needs to be renegotiated. Has Mrs May gone far enough?

What has changed?

Mrs May has decided to put an end to the US authorities’ efforts to extradite Mr McKinnon over allegations that he hacked into military and Nasa computers in 2001 and 2002. It’s the final move in a 10-year legal wrangle.

She also announced that the introduction of a “forum bar”, giving British courts the power to block extradition if they believe the defendant should stand trial here.

And the home secretary will now no longer have the job of deciding on whether extradition should be blocked on human rights grounds. That will be a job for the high court from now on.

What does the McKinnon case tell us about the extradition treaty with America?

Nothing. Mrs May’s ruling was based solely on medical evidence. Mr McKinnon has been diagnosed with the autism spectrum disorder Asperger’s syndrome and doctors said could be a suicide risk if forced to go on trial in America. So the home secretary has stopped his extradition on human rights grounds.

Her decision tells us nothing about the strength of evidence against him, and indeed he could still be charged and tried in this country if that’s what the director of public prosecutions decides.

The ruling doesn’t imply that the US-UK extradition treaty is faulty, and it’s not at all clear that any of the extradition reforms urged by critics would have affected Mr McKinnon’s case in any way.

So what’s the “forum bar”?

Nevertheless, Mrs May does agree that there’s room for improvement in the current arrangements. The big change today is a new power for domestic courts to bar extradition when the defendant could be tried either here or abroad, and the court believes it is in the interests of justice to have the trial here.

This is a major change that could go some way to allaying fears that the US is increasingly looking to extradite over crimes that don’t really take place on US soil – like online crimes that come under US jurisdiction only because US-based internet servers are affected.

We don’t know whether a forum bar would have affected Gary McKinnon, and it may not make a difference to other controversial extradition cases, depending on the exact wording of the legislation.

Sir Scott Baker, the former court of appeal judge who wrote a detailed independent review of US-UK extradition law last year, thought the forum bar that Labour drafted in 2006 but never implemented could lead to more delays and more legal wrangling.

Mrs May says she wants to avoid that so she will draft a different change in the law.

Is the treaty still unfair?

Several MPs expressed displeasure that Mrs May hasn’t torn up the extradition treaty and started again. We FactChecked the fairness debate before and most of the arguments remain the same.

The big complaint from many critics is that the standard of evidence US prosecutors need to show to get someone extradited back to the States (“probable cause”) is less than the equivalent test for UK prosecutors (“reasonable suspicion”).

But the Baker review concluded that there was “no significant difference” between the two tests.

They are worded differently because the Fourth Amendment to the US constitution uses the words “probable cause” and the English legal tradition is different, but the strength of evidence required is the same, according to Sir Scott.

Some critics want the bar to be raised from “reasonable suspicion” to a prima facie case: evidence strong enough to convict someone if not disproved. But that would undoubtedly go too far the other way, putting US citizens at an unfair disadvantage.

Other accusations of unfairness hinge on the numbers of British citizens extradited to the US compared to the other way around.

The latest figures from the Home Office are that, between January 2004 and October 2012, Britain extradited 92 people from the UK to the US and only 43 were extradited from the US to the UK.

The US embassy’s explanation for this is that the country’s population is five times bigger, so there will always be more criminals who go on the run abroad and need to be brought back – an argument that makes perfect sense if most people sent from Britain to the US are Americans who fled the jurisdiction.

If most of the people flown to the States are Britons like Mr McKinnon, that argument rather breaks down, but the Home Office hasn’t given us a breakdown of nationality.

The only insight we have is a freedom of information answer from 2010 which showed that nearly half the people extradited from Britain to the US between 2004 and 2010 were British nationals or had dual citizenship, but only about 10 per cent of people sent the other way were US citizens.

That does suggest that there is an imbalance but it doesn’t prove that this is the fault of the extradition treaty. Perhaps US prosecutors are just more zealous than their British counterparts about pursuing suspects in other countries.

On the other hand, while the British authorities have refused at least eight extradition requests since 2004, the Americans have made no refusals that we know of, so it seems that a British resident has a better statistical chance of avoiding extradition.

What are the implications for other high-profile cases?

A spokesman for the Ecuadorian embassy, currently playing host to Julian Assange, said today that Mrs May’s decision should also be applied to the WikiLeaks founder, who is fighting extradition to Sweden on the grounds that he could ultimately be tried for leaking diplomatic cables.

A spokesman said Mrs May’s decision “was based on concerns that extradition to the United States would see human rights being breached… specifically it invoked article three of the human rights act which outlaws the use of torture and degrading treatment”.

But Mrs May said her decision was based purely on evidence that Mr McKinnon is mentally ill and a suicide risk. It had nothing to do with worries about Mr McKinnon being tortured or treated badly.

This explanation also means that his case is not exactly comparable with that of Syed Talha Ahsan, a British citizen who was extradited to the US earlier this month over terror allegations despite also reportedly having been diagnosed from Asperger’s sydnrome.

Assuming there were no medical reports of serious illness and risk of imminent self-harm in his case, Mrs May can accurately say that the two cases were not the same, though that is unlikely to satisfy the critics who have accused her of double standards and indeed racism for failing to intervene in his case.

By Patrick Worrall