But on past performance, it still has a way to go before it will be satisfied with polling under Mr Little. The caucus forced David Shearer to resign in 2013 despite the fact that Labour's average vote under his leadership was 33.62 in the Digipoll survey.
The latest polling took place during a particularly bad period for the Government, between August 14-24.
There were nationwide protests against the Trans Pacific Partnership talks, the Auditor-General decided to launch an inquiry into the Government's Saudi sheep deal and the Opposition was highly effective at capitalising on ludicrous high-risk industry classifications under health and safety legislation.
Despite the Government's bad month, Labour's gain has almost certainly been at the expense of other Opposition parties, not National which is on 50.8 per cent and could govern alone if the poll were converted to seats.
The number of people who think the Government is moving in the right direction has decreased from 55.3 per cent in April to 50.9 per cent now, and those who think it is not moving in the right direction has risen from 36 per cent to 40.9 per cent.
The poll was completed before the extreme volatility in global share markets, which usually has an unsettling effect on confidence levels.
Prime Minister John Key remains preferred Prime Minister by a country mile, at 63.7 per cent.
Perhaps the bad news for Mr Little is that his popularity has barely moved: last December he rated 13.6 per cent, in April 13.9 per cent and now 13.3 per cent.
New Zealand First leader Winston Peters has maintained the boost he got out of the Northland byelection win in March. He has gone from 5.9 per cent last December to 12 per cent in April and is now on 11.6 per cent.
Labour frontbencher Jacinda Ardern is now the fourth preferred Prime Minister at 3.9 per cent, a jump from 0.5 in April.
Party vote results: National 50.8 (down 0.2), Labour 31 (up 2.3), Green 9.2 (down 1.6), NZ First 6.9 (up 0.8), Conservatives 0.6 (down 0.5), Maori Party 1 (up 0.2), Act 0.2 (down 0.6), United Future 0 (no change); Legalise Cannabis 0.2 (up 0.2), Mana 0.2 (up 0.2).
• The poll of 750 eligible voters was conducted between August 14-24. The Party Vote is of decided voters only. Undecided voters were 12 per cent.
The poll has a margin of error of plus or minus 3.6 per cent.
English voters' pick to replace Key if he quits
Voters would prefer Deputy Prime Minister Bill English to become Prime Minister if, for any reason, John Key stepped aside this term, according to the latest Herald-DigiPoll survey.
Deputy Labour leader Annette King would be first choice as Opposition leader if Andrew Little were to step down, but almost as many would prefer Jacinda Ardern.
Mr English had twice the support of Steven Joyce and was well ahead of Paula Bennett, who is being groomed for a future leadership or deputy leadership role, and ambitious Tauranga MP Simon Bridges.
Mr England has been in Parliament since 1990 and has been Finance Minister since 2008.
The rise of Ms Ardern in the Labour succession question suggests that she would be a popular choice as deputy leader in November when Ms King is due to step down. Ms Ardern has also risen in the preferred Prime Minister rating, jumping 3.4 points to fourth behind New Zealand First leader Winston Peters.
Ms Ardern has responsibility for small business, as well as justice, children, arts, culture and heritage.
She has been a list MP since 2008, standing in Auckland Central against National minister Nikki Kaye.
She has never stood for the Labour leadership in the three contests since 2011 but was on Grant Robertson's ticket after the general election last year and he had anointed her as his deputy.
Neither Mr Key nor Mr Little is expected to step down.
