The CWU decision to call a ballot comes after Royal Mail announced it was planning a pay freeze.
The union said it has seen plans Royal Mail is to cut between 8% and 20% of staff across the country. The CWU said London would be hit the hardest with 1,600 jobs at risk.
Martin Walsh CWU London divisional representative said: "These are arbitrary cuts by management. There's no machinery coming in to help cope with the workload so these job cuts will have a bad impact on services.
"We're balloting our members across London for strike action to fight these cuts."
However, in a letter to the union Royal Mail's human resources director John Millidge said Royal Mail has been badly affected by the recession.
Royal Mail said the UK postal market is declining between 8% and 10% compared to a year ago. It said each percentage point dropped meant a decline of £7m in revenue.