Plans to build a new 8,000 seater stadium Wimbledon Park were approved by the Greater London Authority in September last year.
Campaign group, Save Wimbledon Park, says the plans are too big and the environmental damage would be significant.
Their High Court legal action against the GLA over its decision to grant planning permission for the expansion was dismissed in July.
The group says it is “delighted” to be able to appeal that decision although a hearing date has not been set.
The All England Club says the plans “will create a permanent home for the Wimbledon Qualifying Competition.”
The GLA says “It will create new jobs, public green spaces and cement Wimbledon’s reputation as the greatest tennis competition in the world.”



