A vote for “Brexit” next week looks likely:

Support for leaving the EU is strengthening, with both phone and online surveys reporting a six-point lead, according to a new pair of Guardian/ICM polls.

This is consistent with other polling released over the weekend, including one survey that gave Leave a ten-point advantage. Once the latest ICM result is included, Leave now leads in the polling average by its largest margin to date:

Prof John Curtice of Strathclyde University, who analyses all the available referendum polling data on his website whattheukthinks.org, noted that, after the new ICM data, the running average “poll of polls” would stand at 52% for leave and 48% for remain, the first time leave has been in such a strong position.

As the referendum debate has focused more on immigration, Leave has gained ground, and that has been helped by the backing of a large bloc of Labour voters. Labour leaders have started trying to do more to help the flagging Remain campaign, but their effort is hampered by the fact that roughly half of their voters don’t know what the party’s position is. Gordon Brown has been recruited once again to make a last-ditch appeal, but his clueless handling of questions on immigration seems more likely to hurt Remain’s chances in the closing days.

Obviously, the polling may be wrong. European elections in the U.K. are typically low-turnout affairs, and an EU referendum is likely to be the same, but no one can be sure of that. Because the referendum is a comparatively high-stakes vote, turnout could end up being higher than expected, and both sides assume that would help Remain. Nonetheless, the surge in support for Leave over the last few weeks appears to be real, and Cameron is just ten days away from what could be the most humiliating political defeat of his career. Just as he miscalculated on the independence referendum two years ago in an attempt to squash Scottish nationalism, he has once again tried to bury the Euroskeptics with a vote that they are now on track to win.

It is hard to see how Cameron could retain his party’s leadership after campaigning against what most Conservatives want and losing. There will almost have to be a leadership contest, and Cameron seems likely to lose it. No matter who the prime minister is, he will have a difficult time ignoring a clear majority result for leaving the EU.