Wandsworth is the second worst borough in London for getting children into their parents' first-choice primary school.
Figures released in a report by the Pan-London Co-ordinated Admissions Scheme show 69.4 per cent of parents secured their preferred choice of school last week.
This is just above the lowest borough, Chelsea, where 64 per cent of parents were able to secure their first choice of school, compared to the average of 78.7 per cent.
The report said: "There is unprecedented demand for primary school places across London.
"Nevertheless, all London boroughs are working hard to ensure that every resident child who needs a school place in September is offered one."
Alex Bremer, company director and founder of Silicon Junction, said he has been forced to put his son in private education after being unable to secure a place in a primary school he was happy with.
Mr Bremer, who lives in Battersea, was hoping his four-year-old would go to Belleville Primary School, in September but was offered a place in Christchurch Primary School, Battersea, which was not on his list of choices.
He said "It is a little disconcerting, disappointing, when you think you have lived here for a long time, paid a lot of council tax and made sure you live close to schools when we wanted to start a family.
"They sent leaflets saying how to choose. It would appear Wandsworth Council has not paid any attention and offered the one school near where we live we were least keen on.
"It is very disappointing, we would hope to be served better by our local authority and it is very alarming. There needs to be more schools and better schools."
Another mum, who wished to remain anonymous for fear she would minimise her chance on a waiting list, said she was desperate for her children to get into the bilingual school, Wix Primary School, Wandsworth.
But there were no places available for her children because the majority of spaces were taken up by siblings.
She said: "We are devastated, we moved house from Richmond and showed a commitment to the area.
"We want to develop a relationship with our family in France, who can only speak French so the children can speak to their cousins.
"Our house looks onto the playground, we made a commitment to the community in order to secure a place. The sibling cap should be 75 per cent."
Wandsworth Council was awarded £5m earlier in the year from Central Government to help pay for additional school places.
The squeeze on places is being blamed on an increasing birth rate and parents applying from outside the borough.
There are now 5,200 children being born in Wandsworth each year, in contrast to 4,000 in 2001.
Plans for a free school for 420 primary children on the site of the former Putney Hospital is expected to open in 2015 to ease the strain.
There will also be a school opening in the Professional Centre, Franciscan Road, Tooting sponsored by Graveney School well as a Jewish free school in Southfields by 2013.
Have you experienced problems securing a primary school place? Contact arucki@london.newsquest.co.uk or call 020 8722 6344
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