The postponed campaign, in support of its Adventure Days tickets to London, will run later in the summer.
Other regional operators, including Thameslink and South West Trains, have pulled or postponed ads. Intercity operators Virgin Trains and GNER are pressing ahead with campaigns.
The Association of Train Operating Companies (ATOC) is putting off several consumer PR exercises for the time being, although a promotional offer through WH Smith will continue for a week, as planned.
ATOC commercial director Philip Benham said it was too early for the group to consider a co-ordinated response.