The strike will go ahead following a vote in favour of action by RMT union members. However, London Underground claims just three people voted for it.
Control room staff will walk out from 9pm on Monday (28 September) until Wednesday (30 September) at 11pm, potentially bringing blocking one of the capital's central arteries connecting the City with the suburbs.
Transport for London said it was working on its "resilience plan to minimise impact" and keep disruption to a minimum, but it could not confirm if the line would be kept up and running during the strike.
"We are working on our resilience plan to minimise the impact on the line should this unnecessary strike action go ahead. We’ve been in extensive discussions with the RMT over this issue during the past year and we’ve presented various options to bring this dispute to an end," said TfL.
"These have included exploring development opportunities to help progress the careers of the staff concerned as well as allocating additional responsibilities that would justify a salary increase.
“Unfortunately all of these options have been rejected outright by the RMT who appear determined to demand more money for no additional work or responsibility. We remain committed to discussions with the RMT representatives and I urge them to consider the options we've proposed rather than threaten industrial action," a spokesperson added.
RMT secretary Mick Cash said in a statement: "London Underground (LU) management must be clear by now on our members legitimate and reasonable demand for re-grading. The union has re-iterated that we will not accept an offer which is based on a change in staff duties or which would cause a detriment to other members. Although LU has declined our request for arbitration at Acas, they are aware that as always we remain available for talks to resolve the dispute."
Train drivers will not be involved in the strike and TfL says there are just eight control room staff working on the line, which connects Bank and Waterloo stations, six of whom are RMT members.
RMT could not be reached for further comment on the number of staff involved at the time of publication.