The diocese is hoping to address the shortage of school places for local families.
In Whiteley, where one of the schools is to be opened, some parents face the prospect of having to drive two hours a day to and from schools in Fareham.
There are plans to open a primary for 30 extra students on a temporary site between Leafy Lane and Lady Betty's Drive in September next year.
The class of 30 four-year-olds would be increased by 30 new pupils each year until the school is at capacity.
The plan is to eventually move the primary to North Whiteley where up to 3,000 new homes will be built in the next few years.
The plans were welcomed by Laura Poustie, who is mum to Niamh, 3, and Lewis, 1.
She said: “Niamh will be going to school in September 2014, and we’ve got the figures to show that’s a bumper year across the whole of this part of Hampshire. The need for the school is huge, and it’s brilliant that we’re going to have a school here. The site might not be ideal, but it’s only temporary, and the new permanent site will be better. The alternative is not just having to go out of Whiteley, but also that your children might not end up at the same school, which means you start having to put them in breakfast clubs and after-school clubs. To me, a school is actually a focus for the community, as you do make friends at the school gates. That’s more difficult if you’re doing it away from where you live. And I like the fact that it’s a faith school because I like the idea of assemblies and celebrating Christian festivals.”
Jon Mayhew, whose daughter Imogen, 3, will start school in September 2014.
He also welcomed the planned school and its faith ethos.
He said: “It’s important to us because it affects Imogen and lots of our friends who live even further from Whiteley Primary than we do and have no chance of getting in. It will be nice for our children to have a degree of faith in their education. It’s good that the entrance criteria won’t be based on faith, but that there will be assemblies, prayers and festivals celebrated.”
Alison Allwood, who is mum to William, 2, and two-month-old Emily, said: “We want our children to be going to a school where they live, where they can walk to school and where they can go with their friends who live nearby. My friend takes an hour to get to St John the Baptist Primary in Hunts Pond Road and back every day.”
Despite the huge demand for school places in Whiteley, Hampshire County Council was unsuccessful in its 2007 attempt to buy a suitable site for a new C of E primary.
Then in 2011, there was another setback when the Portsmouth Diocese's application for a C of E free school in the town was turned down by the Government.
This year, the diocese consulted with residents about a voluntary aided school that could be opened within a year.
The proposal has the support of local residents and the Diocesan Board of Education has now approved plans and issued a public notice.
Hampshire County Council is expected to make a final decision on it in January.
In addition the diocese has applied to the Government to open a new 420-place academy near Waterlooville in September 2014.
The Church of England school, which would take in four to 11-year-olds, also has strong local support.
Research by the diocese found that 86 per cent of locals were supportive or very supportive of the plans, and 84 per cent had no reservations about a C of E faith ethos for the school.
The diocese will find out next month whether its application has been successful.
Local churches would also hope to employ an ecumenical community worker, who could point residents to the various existing churches of all denominations.
Portsmouth’s diocesan director of education Tony Blackshaw said: “We’re excited about the possibility of providing schools with a Christian ethos in these areas where they are really needed – not just to provide good education, but also to act as a focus for these communities.”