Yvette Cooper's bid to become the next Labour leader has been given a boost after party grandee Alan Johnson threw his support behind the former work and pensions secretary. Johnson, a former home secretary and trade union leader, is a popular figure within the party and his endorsement is likely to draw support to Cooper as the leadership race hots up.

Johnson, who will head Labour's pro-EU campaign ahead of the promised referendum on the UK's membership of the 28-nation bloc, heaped praise on Cooper for her "experience" and "inner steel". The Hull West and Hessle MP also argued she would bring economic credibility to the top job.

"I've been enormously impressed by her poise, command of her brief as shadow home secretary, and her ideas on tackling inequality, child poverty and a radical programme of genuine devolution," Johnson wrote in The Guardian.

"She's defended our economic record against the crass lies of those who suggest that Labour created the global financial meltdown; and she understands the crucial difference between pretending that the fiscal deficit can be ignored and planning to reduce it on a timescale that doesn't choke off growth and hit the poorest hardest."

The intervention comes after a private poll, leaked to the Daily Mirror, put left-winger Jeremy Corbyn 20 points ahead in the leadership contest, with Cooper in second, former favourite Andy Burnham in third and shadow care minister Liz Kendall trailing in last place. The release of the data was significant because, with second preference votes taken into consideration, Cooper would only be two points behind Corbyn (51% vs 49%).

The poll subsequently strengthened Cooper's credentials as the anti-Corbyn candidate in the race as the socialist firebrand has seen a surge in popularity and the most nominations from local Labour parties (152). The Islington North MP has also won the backing of two of the UK's biggest trade unions, Unison and Unite. However, due to Labour's "one member, one vote" policy, the union support and local party backing only serves as an indication of Corbyn's electoral strength.

The latest independent poll, commissioned by The Times and conducted by YouGov, predicted Corbyn held a 17-point lead over Burnham (43% vs 26%), with Cooper on 20% and Kendall on 11% based on first preference votes. Labour will announce Ed Miliband's successor at a special conference on 12 September, the day before the party unveils its candidate for the 2016 Mayor of London election.