Children should be allowed to attend school from as young as two, to counteract generations of educational disadvantage and poor social skills, according to Lady Sally Morgan, the head of Ofsted.

Morgan, a former Cabinet Office minister and adviser to Tony Blair, called for a "big bold brave move" to target funding at educational underachievers, and the establishment of a new type of "all-through" school to educate pupils from two or three up to the age of 18.

Citing research by Ofsted, Morgan told a meeting in London organised by the Ark academy chain: "Poor under-fives are still 19 months behind their affluent peers when they start school at five. What a dire start to their educational lives.

"Those children have low-level social skills, especially reading and communication. They're not ready to learn at school. Weak parenting, low educational attainment of parents, poor diet, poor housing and so on, the gap between affluent and disadvantaged is greatest in that group."

Morgan said there was a political imperative to help children from poorer backgrounds, alongside Ofsted's introduction of a tougher regime of inspection for daycare and nurseries.

"I think there needs to be a big bold brave move on the under-fives agenda to target funding heavily on the children who will benefit most and – increasingly I think – to look to strong providers to go further down the system.

"We've increasingly got five-to-18 schools, why not [from] three?" Morgan said, later adding: "I said three to 18, it could be two to 18 as far as I'm concerned."

The comments by Morgan, who became chair of Ofsted in 2011, will fuel controversy about the expansion of schools into supportive roles that were previously the domain of parents.

Sir Michael Wilshaw, Ofsted's chief inspector of schools, has previously said that where parents are unable or unwilling to help with their children's education, schools should have to step in.

Morgan echoed Wilshaw's comments, saying: "At the moment, a lot of children from really disadvantaged backgrounds aren't ready to learn, so the school almost has to provide nurturing before it can start to educate."

Many school nurseries already offer places to three-year-olds, with the government funding a minimum of 15 hours a week of childcare in schools or through private providers. But rising primary school enrolments and council funding cuts mean many schools have reduced their nursery provision to four-year-olds.

Recently the government has offered similar funding to parents of two-year-olds in households on income support or earning less than £16,000.

The Department for Education said it was allowing schools to expand nursery places to include two-year-olds. "We know that teacher-led early years education has a positive impact on children, especially on those from low-income backgrounds," a spokeswoman said. "That is why we are making it easier for schools to take children from the age of two by removing the requirement on them to register separately with Ofsted when doing so, and introducing 15 hours of free early education for 240,000 of the poorest two-year-olds."

The DfE pointed out that 96% of children now received 15 hours of week of education at the ages of three or four. "In addition we have strengthened early years qualifications and today Ofsted has introduced a tougher early years inspection framework to help drive up quality in childcare," it said.

But Morgan said policymakers "haven't really taken a grip of this problem," with most of the effort being aimed at improving the education of those over the age of five and already attending school. "We haven't got much improvement in provision for the under-fives," she said.