Strike action could happen in the coming weeks if talks over wage rises stall.
Separately, about 2,500 members of the Transport Salaried Staffs' Association also voted in favour of strike action on Monday.
The RMT has resumed talks with Network Rail, which owns and operates the UK's rail infrastructure, as well as the train companies over pay rises. The RMT recently told the BBC that it is "not in any rush" to call for further strikes in July.
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