Harrow Borough Council says it is determined to deliver a fair start for every child as it plans further rounds of school expansions.
The comments come after the Harrow Times reported last week the council was planning to permanently expand more schools to meet the demand for places.
Proposals for the second round of school expansions are currently being put through planning with some set to open with more classes in September.
Cabinet member for schools Cllr Simon Brown said: “By this time next year, we will have provided almost 5,000 new, permanent primary school places in Harrow.
“It is a Herculean effort, which is delivering more than £100m of government investment to benefit Harrow’s families.
“But our population is still rising, and even more places are needed.
“We are determined to deliver a fair start in life for every child in Harrow at a good, local school – and so our work must continue.
“It appears clear that Harrow may not only need a third – but even a fourth phase of school expansions.”
The council predicts Harrow will need seven further reception forms of entry in 2015, rising to ten forms in 2016 and 13 forms in 2017.
It is hoped the free school applications currently being processed will which would deliver five forms of entry and help meet demand if approved.