When most people leave a job they generally follow one simple rule: don't burn any bridges. But TV talk show host Cenk Uygur is not obeying this unwritten law.

Instead, he has accused the US liberal TV channel MSNBC of bowing to political influence by axing him in a bid to silence his criticisms of politicians. "They are concerned with access … MSNBC needs to get those [political] guests," he told the Guardian. "The minute you step outside and attack the whole system and say the whole system is corrupt, then you've got a problem. That was the problem I ran into," he said.

The fiery presenter had filled in for the recently departed liberal icon Keith Olbermann in his daily prime-time show. He had done well in the ratings with a strident, hyper-critical style that slammed the usual Republican targets but also did not spare Democrats, especially President Barack Obama.

In the world of American political cable TV, Uygur's voice was loud, proud and leftist: providing a rare mirror image to Fox News's conservatism, not only in substance but in uncompromising style.

But in June, MSNBC's boss, Phil Griffin, told Uygur that he was not getting Olbermann's slot on a permanent basis. That prompted Uygur to reject an offer of a reduced role, walk out of the network and go public with his accusations. Cenk did not burn his bridges with MSNBC, so much as nuke them. His claims caused a major media storm with some lining up to back Uygur, but many more slamming him as unable to take criticism and offering no proof for his story.

Uygur, 41, is not backing down. He believes he was silenced for going too far rather than just playing the usual partisan game of attacking familiar Republican targets. He said he turned down an offer to stay on at MSNBC with a weekend show because he wanted people to understand that the media they were watching was not free of outside influence. "I want people to know what the reality is. When they consume the news on TV they have to understand it is coloured by so many other factors. There are advertisers, parent corporations and issues of access to politicians. All of that gets mixed up with the facts," he said.

Uygur insists – despite MSNBC's denials – that Griffin told him personally in a meeting that his combative style had angered politicians in Washington. "[He said], 'We are insiders. We are part of the establishment. Washington is concerned with your tone,'" Uygur said, adding that he could barely believe what he was hearing. "I thought: 'Are we in a movie? Is this for real?'" he said.

For his part, Griffin told the New York Times in July that he meant that booking guests for Uygur's show had become increasingly difficult because guests were put off by Uygur's style and combativeness. His reference to "Washington" was simply describing the show's producers in the capital. The White House, too, has said it would never try to interfere with a network's content or presenters.

But Uygur says he has no doubt about what Griffin really meant. "It was clearly politicians of some sort," he said. He points to the fact that his ratings – while not spectacular – were solid. His supporters also believe that it is significant that Uygur's replacement, the Rev Al Sharpton, has given an interview in which he said that he would not criticise Obama.

Uygur's outspoken criticism of MSNBC has earned him a legion of critics. Howard Kurtz, CNN media correspondent and the Daily Beast's Washington bureau chief, attacked him in an interview and numerous bloggers accused Uygur of mistaking the personal for the political. Yet Uygur's story is not just about the style and tone of the American media and the issue of outside interests and "access journalism".

It is also about how the rise of the internet and social media can sidestep traditional journalistic outlets – Uygur is now focused back on his old job, hosting the popular internet and radio show The Young Turks. The show gets more than 28 million views a month and has more than half a billion total views on YouTube. Uygur believes that means you can burn your bridges – at least with traditional media – and still have a powerful voice.

"It is a brave new world. In the old days if they removed you from TV you were done," he said. The Young Turks, intended to be supported mostly by YouTube advertising, is free from outside influence, he added. "This is unfiltered news. This is news that does not care about sucking up to politicians and the powerful."

It is also Uygur's first love. The Wharton-educated, Columbia Law attorney – and former Republican – founded the show in 2002 when it premiered on Sirius Radio, before it took off on YouTube. It covers politics and culture and Uygur boasts that its one million views a day puts it on a par with a lot of the cable news shows. He says the younger viewer profile of an online show also fits in with his more liberal views than the older, more traditional audience members who tune into cable news.

"Online progressives are more informed and more aggressive. They can't wait to take on power," he said. Certainly Uygur has not let his experience of losing his MSNBC show dent his ambitions to have a loud voice in politics. It has just thrust them into a different arena. "I am quite ambitious," he joked. "Our plan for The Young Turks is total media domination. We are the largest online news show in the world. My goal is to be the largest news show. Period."