Tony Blair has delivered his most damning verdict on Gordon Brown's government to date, claiming New Labour died when he left office in 2007 and that the party "lost its driving rhythm".

The former prime minister said the 13-year Labour government should be remembered in two phases – his and Brown's – and there was "no continuity" between the two.

In a speech in London to the New Labour thinktank Progress, Blair also advocated a "pick and mix" of policy that did not adhere to old narratives of left and right. He urged the party to let go of some of its old ideologies in order to arrive at the "right" policy decisions.

He said: "I remain unremittingly an advocate of third-way, centre-ground, progressive politics that came to be called New Labour. From 1997 to 2007 we were New Labour. In June 2007 we stopped.

"We didn't become old Labour exactly. But we lost the driving rhythm that made us different and successful. It was not a government of continuity from 1997 to 2010 pursing the same politics. It was 10 plus three."

It is the most comprehensive analysis Blair has made distinguishing between his and Brown's premiership. He also stressed his support for the Labour leader, Ed Miliband, but warned that the party could not indulge in the "politics of protest".

He said: "Parties of the left have a genetic tendency to cling to an analysis that they lose because the leadership is insufficiently committed to being left, defined in a very traditional sense. There's always a slightly curious problem with this analysis since usually they have lost to a rightwing party. But somehow that inconvenient truth is put to the side.

"This analysis is grasped with relief. People are then asked to unify around it. Anything else is distraction, even an act of disloyalty. This strategy never works."

Recalling his government's policies to introduce academies, more patient choice in the NHS, asbos and university top-up fees, plus its pro-business stance – all of which were controversial on the left of the party – he said: "Some of these policies could be supported by people who don't vote Labour. That's not a bad thing.

"In the real world of the 21st century there will be some pick and mix of policy. Sometimes it will be less left v right than right v wrong. Above all today, efficacy – effective delivery, motivated of course by values – matters as much if not more than ideology. Don't fear it. Embrace it. It liberates us to get the correct policy."

He argued that Labour should make the economy its priority. "I still think we need to focus a lot on the micro side: targeted policies that support business, jobs, that allow that large amount of cumulative reserves in business to be invested and that also gives us an opportunity to regain, which I think is very important to us, our relationship with business."