It is the second major jobs bombshell from the historic company and follows the axing of its city centre call centre in Aldermanbury with the loss of about 500 jobs.
The latest closure plans will hit effect 150 staff - some of whom survived the previous cull.
Thomas Cook said transfer of work from Birkenshaw to its Peterborough base would begin from next month, with the office in Inmoor Road due to close by the end of January 2015.
Staff at Birkenshaw, including 76 who were transferred from Aldermanbury when it closed, have been told of the planned move and a 45-day formal consultation period will start from Monday.
These will include details on when any changes may occur and where each function will be located.
Plans involve migrating back office and support functions from Birkenshaw to Peterborough throughout 2014.
Some functions could cease or be outsourced, depending on operational changes.
The company said the decision had been reached after considering several options under its ‘location strategy review’ and closing Birkenshaw was seen as the most effective as the group strives to get back on track after its bankers nearly pulled the plug.
Thomas Cook said customer service levels would not be affected by the closure plans and it would explore all options for staff, including possible relocation or redeployment opportunities.