RMT members at Heathrow Express were set to strike again on Wednesday of this week for 24 hours from 3am.
It is the third wave of strikes since bosses announced a multi-million pound cuts package.
Two hundred workers are under threat of redundancy while those who remain face a ten-year pay freeze.
Bosses also want train drivers to take on the role of evacuating passengers in an emergency so they can get rid of other onboard workers.
A planned 24-hour strike last Saturday by RMT members working for Rail Gourmet on East Midlands trains was suspended for talks. The dispute is over disciplinary procedures.
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