A free school in Mortlake was opened by MP Zac Goldsmith last week.
Thomson House School in Sheen Lane is a new two form entry, primary free school.
The Conservative MP said: “Richmond’s primary schools are among the best in the country, but there is a real shortage of places and I am therefore thrilled to have supported Thomson House from the start.
“It will be a fantastic school at the heart of the local community, and I wish it well.”
The school was set up by a group of parents including the head of prep at the Harrodian School, Matteo Rossetti.
Pupils at Thomson House have access to the Harrodian School’s sports grounds as well as their gifted and talented programme.
The school will grow each year until it reaches its full capacity of 364 students.