Additional reception places for little learners will be made available from September after parents were shocked to be told of a major shortfall in school places.
The places will be at Joseph Hood Primary in Whatley Avenue and West Wimbledon Primary in Bodnant Gardens.
The news comes after charity Chapel St announced it would open a new free school in Merton Park but it would not open for another school year.
Park Community Free School hopes to run out of Tyndale House, in Dorset Road, Merton Park, with two reception classes by the start of next year's autumn term.
Parents hoping their children will be able to join reception at the school this year received letters advising them to accept a place at an alternative school until a temporary site is found.
Councillor Martin Whelton, cabinet member for education said new places in existing schools was welcome news.
Coun Whelton said: "Parents need to have a degree of certainty and we can’t wait forever."
The council will be sending out a second round of offers to parents within a fortnight which will include the places provided by these two additional classes.
Merton Council’s director of children, schools and families, Yvette Stanley, said: "To ensure children receive a local offer of a school place, we strongly advise parents and carers to contact the school admissions team and add extra schools to their preference list.
"If they do not do this, they risk not getting offered a place at a local school."
Advice for parents can be found on the website.
- AFC Wimbledon mascot Haydon the Womble to take on Spongebob on Nick Kicks this morning
- Stop cold calls with a text OR use our 11 funny ways to deal with them instead
- Two companies likely to provide waste collection in four boroughs
- Prison officer and inmate's girlfriend smuggle heroin, cannabis and mobile phones into Wandsworth Prison
- World War 1 footage and historic photo exhibition some of the highlights of day dedicated to Merton's heritage