The BBC needs "clearer red lines" around its website to allow competitors that depend on private revenue to survive, the government warned today.

Amid concerns that the government is hostile to the BBC, the culture secretary, Jeremy Hunt, lavished praise on the corporation for helping to ensure that Britain has the best television in the world.

But Hunt raised a series of concerns in an interview with the Andrew Marr Show on BBC1. The culture secretary warned that the corporation:

• Needs to be careful that its website does not crowd out the market. "The web is a very good area where the BBC needs to have clearer red lines about what it will and won't do. I mean, we all recognise that programmes need to have websites. But do we want Top Gear to have a strategy to say 'we're going to be the biggest motoring website in the country?' No, we don't, because that will put off anyone who's got an idea for a website to do with cars from bothering to invest in it."

• Should focus on producing programmes at the high end of the market. "I'd like the BBC – and I've always been very clear about this – to concentrate on producing great TV programmes at the quality end of the spectrum. One of the things I think we get from having a BBC is that there is competition in British broadcasting at the quality end and not just at the mass end of the market."

• Should be open about the salaries of celebrities "so that people can make their own minds up". Hunt added: "We have learnt in government that actually transparency is the best way to solve a lot of these issues because you're saying to the public, look, you're grown up, you make up your own minds. We'll give you all the information you need.

"We're going through a transparency revolution in the government at the moment and that is something that we are welcoming with open arms, and I think the BBC could learn from that."

Hunt stressed his commitment to the licence fee. But he warned: "The way we collect it may have to be rethought, because technology is changing, a lot of people are watching TV on their PCs.

"We're not going to introduce a PC licence fee and that is something that I do need to have discussions with the BBC to see what their ideas are."

Hunt also confirmed that the government had no plan to relax the rules on impartiality for TV news.

Asked whether Rupert Murdoch would be allowed to set up a British version of the controversial US network Fox News, he said: "Absolutely not. We have said – and I announced in opposition – that we are committed to protecting the impartiality requirements amongst the major broadcasters."