Frank Field was very briefly a minister in the Blair years and then argued with Blair over something and went to the back benches. Jeremy Corbyn wasn't. Surestart children's centres were introduced by that government, but many of the people who have tried to take credit for doing so since then, such as Yvette Cooper in the 2015 leadership election, didn't have much to do with it.
Frank Field was then appointed to a post by the Tory-Lib Dem coalition government (!) to look into ways of tackling poverty. He doesn't seem to have even suggested that that government should keep Surestart. In my area the first big round of cuts was in 2011, hitting children's centres that only opened in 2008 and 2009. An academy chain took over a local primary school in 2012 against the wishes of 94% of parents, at the behest of the DfE (and Michael Gove) but with support against the school from the Labour Party. One of the first things the organisation now running the school decided to do: cut children's centre services including some of the best baby and toddler groups in our area. They might have encouraged more families from deprived backgrounds (in this very poor area with some gentrification) to apply to the school, that wouldn't have done at all. My kids' school fought off academisation - the much smaller chain that wanted to take us over wanted nothing to do with our lovely children's centre.
Under Tony Blair and Gordon Brown the last Labour government continued the policies of privatisation, for example housing. In opposition, under Ed Miliband, they didn't oppose Tory and Lib Dem policies such as cutting funding for local government, cutting benefits and increasing sanctions that particularly hit single parents and people with disabilities and carers, among others. My very right wing Labour council from 2010 to 2015 welcomed and went along with forced academisation. Only 6 Labour MPs voted against the Tories' hostile environment legislation in 2014 - including Jeremy Corbyn, John McDonnell and Diane Abbott, and my own MP (who's not as left wing.
That is the background to Jeremy Corbyn's election as leader, many of us actually wanted a leader who wouldn't continue with the policies that had failed under Gordon Brown, who would oppose the Tories in a way that our MPs hadn't done under Ed Miliband.
Also a lifelong Labour supporter here, often frequently demoralised with the Labour Party.