A judge ruled on Friday that a 23-year-old student can be extradited to the United States for running a website posting links to pirated TV shows and films, despite significant doubts over whether such sites break any UK laws.

The ruling threw Britain's contentious extradition treaty with the US, which critics allege is greatly biased against UK nationals fighting their removal to America, under further scrutiny. It came just hours after a businessman from Kent lost an appeal against the decision that he should be sent for trial in Texas for allegedly plotting to send missile components to Iran.

Richard O'Dwyer, a computing student at Sheffield Hallam University, faces a potential 10-year term in a US jail despite never having been to America or using web servers based in the country. When still a teenager O'Dwyer set up a website, TVShack, which posted links to pirated material. It did not directly host any files, which meant, according to the student's lawyers, that it acted as little more than a Google-type search engine and did not breach copyright.

The defence team pointed out that the only UK prosecution of a similar site, TV-Links, ended last year with the case being thrown out.

But the district judge, Quentin Purdy, ruled that O'Dwyer should nonetheless face trial in the US. "There are said to be direct consequences of criminal activity by Richard O'Dwyer in the USA, albeit by him never leaving the north of England," Purdy said. "Such a state of affairs does not demand a trial here if the competent UK authorities decline to act, and does, in my judgment, permit one in the USA."

O'Dwyer said he planned to appeal. His mother, Julia, broke down in tears outside the courtroom, saying the extradition treaty was fundamentally unfair. Describing herself as "disgusted" by the verdict, she said: "Look at how many people we send over there, and how few come here. If they can come for Richard, they can come for anyone."

She added: "David Cameron and Nick Clegg came into office saying they would fix this law," she said. "They need to pull their fingers out."

While O'Dwyer's defence portrayed him as the vulnerable, introspective young man whose promising career would be derailed by extradition, prosecutors contend he is a skilled businessman who made large sums of money from a website he knew was profiting from pirated material.

At its peak, TVShack was among the 1,800 most visited websites in the world, the court heard, bringing O'Dwyer advertising revenue of £15,000 per month. When US customs agents seized the site in 2010 it was replaced immediately with a slightly different domain name – and the addition on the front page of a rap video called Fuck Tha Police. O'Dwyer, who was bailed, said outside court: "I am obviously disappointed with the judge's decision today. I think I have got faith in the high court for making the right decision."

He said the website had "helped me no end with my studies" and said when he first set it up he "didn't even think it would get that popular, to be honest".

The second case concerns Christopher Tappin, a 64-year-old golf club president from Orpington. He admits arranging the shipment of batteries that can be used in Hawk air defence missiles, but insists he had no idea about their eventual destination.

His extradition was ordered last February, even though Tappin's lawyers claim he was the victim of a sting by US agents, who told him they would arrange the necessary export licenses.

Tappin, who said he made around £300 from the deal, appealed against the decision. Two high court judges dismissed this on Friday. "Entrapment, as far as I can see, is simply unsustainable on the facts as alleged in the request," their ruling said.

The best known case thrown up by the extradition treaty concerns Gary McKinnon, the computer hacker who has spent years fighting his removal to the US.

Opponents of the current arrangements, including many MPs, say the fact US prosecutors do not need to present prima facie evidence to gain extradition makes it too easy for British nationals to be sent over, where they often spend long periods in jail before trial.

The US Immigration and Customs Enforcement (ICE) agency has faced criticism for perceived overreach in targeting websites, like TVShack, with no direct US link.

In July the agency's assistant deputy director told the Guardian that ICE would now actively pursue websites similar to TVShack even if their only connection to the US was a website address ending in .com or .net.

Such suffixes are routed through Verisign, an internet infrastructure company based in Virginia, which the agency believes is sufficient to seek a US prosecution.