Rail workers at 14 train operators will strike on 13 May, on the day of the Eurovision Song Contest final, after the RMT union rejected the latest pay deal.
The offer was aimed at ending a long-running pay dispute.
But the union said accepting the offer would have meant no further strike action could take place.
It follows train drivers union Aslef calling strikes on 12 and 31 May, and on June 3, the day of the FA Cup Final.
