Jeremy Hunt is still culture secretary, for now. Despite call of "resign in the chamber!" during his statement to the House of Commons, his position seems slightly more secure than it appeared earlier on today. There are three reasons for this.
Firstly, at the moment he has the prime minister's "full support". Tory backbenchers took a cue from their leader and refrained for baying for his blood, too.
Watch the moment when Cameron threw his weight behind Hunt at PMQs:
Secondly, the resignation of his SpAd Adam Smith meant that Hunt could at least attempt to put some distance between the the News Corporation emails and his own desk. He was able to say that "the volume and tone of those communications were clearly not appropriate in a quasi-judicial process", and then link it straight to Smith's resignation, suggesting that the problem had already been dealt with - always a good move for a politician.
Thirdly, the prime minister is absolutely clear that nothing should prejudice the independence of the Leveson Inquiry. Hunt is currently due to give evidence to it at the end of May, and seems to be suggesting that his resignation prior to his appearance would be to pre-empt its findings. A slightly gymnastic logical leap, it is true, since the Leveson Inquiry will report to Jeremy Hunt as culture secretary. But it's a line that the prime minister is clearly keen on, indicating that there'd need to be another major revelation for Hunt to step down before his appearance.