Labour may have taken the lead in our poll, but the party is far from being ready for government

There is a big gap between the scepticism of the wider public and the adulation for Mr Corbyn personally among the party faithful

The British public have made a turn to the left of politics (PA)

Labour has taken a five-point lead over the Conservatives in the latest BMG poll for The Independent, and more people say they would prefer Jeremy Corbyn to be prime minister than Theresa May.

Plainly, it is early in a parliament to be taking opinion polls seriously, and there will be many who have vowed after the last election never to take them seriously again. But there is no better way of knowing what people think, and so the important thing is to learn from the mistakes of last time and to interpret the results carefully.

Our poll tells us some important things about the state of public opinion. One is that the Labour Party under Mr Corbyn is a serious contender for government. It is hard to say whether the Labour lead, and Mr Corbyn’s overtaking Ms May as preferred prime minister, marks the beginning of a shift.

Other recent polls suggest the two parties are neck and neck, and some commentators have expressed surprise that the Conservatives should be so popular after so many negative headlines. But re-elected governments tend to maintain a high level of support for the months after an election. We will have to wait for more polls before we know if ours is an early indication of the onset of mid-term unpopularity for Ms May.

We do know that, if Tory support has dipped, it is not as a result of the Prime Minister’s unfortunate speech in Manchester on Wednesday, as our poll was carried out the previous week, while Mr Corbyn was riding high on Labour euphoria in Brighton. That said, it is worth remembering, as Ms May said in her speech, “Many pay little attention to great conferences and gatherings like this.”

So there are two reasons for Labour to hold any temptation to triumphalism in check. One is that the next election is probably four and a half years away. Remember what politics looked like just six months ago, before the publication of the manifestos, with Labour trounced in the local elections and Ms May heading towards a Commons landslide with average 19-point leads in opinion polls.

The hardest part of the Brexit talks is yet to come and, if we ever do leave the European Union, politics will look completely different then.

The other reason for Labour caution is the tempered enthusiasm for Mr Corbyn as possible prime minister. True, he now leads Ms May narrowly, by 32 per cent to 30 per cent, but almost as many people, 27 per cent, say, “Neither of them.” And a further 11 per cent say they don’t know. Between them, the Neithers and Don’t Knows have it.

This is where Mr Corbyn needs to do his hardest thinking. There is a big gap between the scepticism of the wider public and the adulation for Mr Corbyn personally among the party faithful who flocked to the Labour conference and to the associated festival of Momentum, a cross between a faction and a fan club.

If Mr Corbyn is wise, he will use this moment of relative success to build up other members of his Shadow Cabinet so that he can present them as a strong and competent Labour team. He has the time to do so.