According to the union in a ballot 22 out of 23 returns were in favour of a strike, while all 23 were in favour of industrial action short of strike.
Staff at newspapers in the area, which covers Surrey, Sutton and Twickenham, have been working to rule since 15 April. In the same ballot they also unanimously voted to continue this work to rule.
The union claims the dispute is over four issues: the reduction in editorial space, redundancies across all sections of editorial, a review of a two per cent pay rise and an office relocation.
Last week the division announced 12 job cuts at a series of titles in the area, including the loss of the sports and leisure department at one of the South London offices.
The changes would mean news, sport and leisure for seven newspapers would be produced by a total of only 12 reporters and two editors, the NUJ said at the time.
Speaking to Journalism.co.uk Mother of the Chapel for NUJ Newsquest South West London, Thais Portilho-Shrimpton, said she was very pleased with the result.
"We are angry because we're seeing our newspapers virtually disappearing, our newsroom disappearing, we expect our news reporters will be asked to take on the work from sports and leisure. The NUJ has already said we don't accept that. That's so detrimental to the quality of our titles."
Newsquest has not responded to a request for comment.