Members of Aslef voted by 4-1 in favour of industrial action over a "serious breakdown" in relations with the company.
The union announced that drivers will strike on Tuesday 21 February and again on Thursday 2 March if the row is not settled.
But the General Secretary Keith Norman raised hopes that strikes could be avoided when he revealed that considerable progress had been made during talks between the two sides.
"During the past 10 days we have had constructive talks and have made considerable progress.
"Because of that progress and the goodwill shown on both sides the Executive has resolved to postpone any industrial action for three weeks."
Mr Norman said outstanding issues yet to be resolved included complaints about bullying and harassment of staff.
Members of the Rail Maritime and Transport union voted by 6-1 in favour of industrial action in the same dispute.
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