Andy Burnham, Labour’s shadow health secretary, said on Wednesday he would stand for the party’s leadership as Britain’s trade unions rushed to secure a big role in electing Ed Miliband’s successor.

Burnham, a bleeding-heart socialist who resists any move toward liberalization of the bloated state health service, is seen as the unions’ favorite and also supported by leftist parliamentarians who believe the party must firmly position itself on the left of British politics to stave off another election defeat.

Labour went down from 257 to 232 seats in the election last week when Prime Minister David Cameron’s Conservatives won an overall majority in Parliament. Miliband stepped down as party leader the day after the election. Labour announced on Wednesday if will hold a leadership contest during the summer and declare the results at a special conference in September.

Centrists are trying to forestall a lurch to the left by arguing that Labour should move back to the centrist policies of Tony Blair who won three elections in a row for the party in the late 1990s and early 2000s. Peter Mandelson, an architect of “New Labour,” said this weekend it had been a mistake to think Labour could wave its fists angrily “at the nasty Tories and wait for the public to realize how much they miss us.” Rather it seems most English voters still didn’t trust Labour to manage the economy after it presided over the 2008 crash while Scotland, a traditional Labour stronghold, overwhelmingly backed the anti-austerity Scottish National Party.

The right wing of the party is likely to coalesce around Chuka Umunna, the Blairite shadow business secretary who announced his candidacy on Tuesday.

Another Burnham opponent could be Yvette Cooper, the shadow home secretary, who is expected to declare her candidacy on Thursday.

Labour’s trade union allies played a key role in electing Ed Miliband as leader in 2010 and are likely to have a significant influence again this time around.

Miliband changed the way Labour elects its leaders, denying the unions a guaranteed one third of the votes. But the new one-member-one-vote system could inadvertently give them even more power as it allows union members to affiliate for free and gives them the same voting rights as paying party members.

The Financial Times reported on Monday that Unite, which represents some three million workers across the United Kingdom, was busy signing up members to influence the leadership race.

One official estimated that 400,000 people might vote in the leadership contest. Of these 250,000 could be union members, roughly in line with 2010.

If centrists like Cooper and Umunna split the New Labour vote, the party could end up with Burnham as leader who is unlikely to move Labour back to the middle.