Studies show the primary population in the borough will increase by 20% between 2012/13 and 2017/18.
The council says it is making sure it can meet this demand with the expansion and building of new schools, with plans to create more than 1,690 primary places by 2023.
Children services boss at Hammersmith & Fulham Council, councillor Sue Macmillan, said: “We are determined to help parents and guardians secure outstanding places for their children by giving them more choice.
“We are helping existing schools expand and supporting the creation of others to ensure children in our borough have the best possible start to their educations.”
Among current schools expanding are Burlington Danes Primary Academy, which will take its first 60 reception pupils in September this year, and the expansion of St Stephen’s School in Shepherd’s Bush, both in the north of the borough.
Further south there will be expansions of Holy Cross and St John’s primary schools, while Sulivan Primary School was saved from closure last year.
As part of its effort, the council says it is also working hard to stop parents who falsely claim to live in the area in order to get their child into a particular school, with officers cross-checking council tax records with the addresses of applicants of all over-subscribed schools and investigate any discrepancies.
This year, 74% of parents and carers were offered their first preference for their children, 90% were offered one of their top three choices and all received a place. There were 1,488 applications for a primary school places this year.