The strike on 19 June will disrupt mail deliveries across the city.
The postal workers are claiming that "arbitrary" job cuts will affect about 1,600 workers and that staff may be downgraded into part-time positions.
But Royal Mail dispute the job cut figure and say a fall in mail volumes meant fewer jobs were needed.
A Royal Mail spokesman said the changes being put in place were already agreed with the CWU as part of the 2007 deal.
CWU deputy general secretary Dave Ward said that Royal Mail is blocking modernisation by refusing to negotiate change with the CWU.
But the Royal Mail spokesman said: "A strike will not modernise Royal Mail - it will simply disrupt the service to which customers are entitled, lead to an even greater loss of business and leave Royal Mail far less able to protect full time jobs.
The spokesperson added that productivity in Royal Mail offices in London already lags behind the rest of the UK with the productivity in parts of London now 10% worse than the UK average."
The London strike would come at a time when the Government's planned sale of a minority stake in Royal Mail to a private company may be delayed to increase the price.
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