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Most train operators will start running services later than usual on Tuesday morning, but aim to return to normal timetables later on.
However, Avanti West Coast will run a severely limited service all day.
Walkouts over pay and conditions by union members - planned for 5, 7 and 9 November - were cancelled on Friday.
But there has still been widespread disruption to services, and operators said people should check trains were running before travelling.
Avanti said its services between Euston and Manchester, Liverpool, Birmingham and Preston, would operate on a limited timetable, starting just before 08:00 GMT.
Its last train north will depart Euston mid-afternoon.
The reduced timetable will mean North Wales, Shrewsbury, Blackpool and Edinburgh have no Avanti West Coast services. The disruption is likely to continue into Wednesday and Thursday, Avanti said.
Rail operating companies were informed on Friday that the strikes would no longer take place.
However, it takes time to rebuild a timetable and ensure rolling stock is in the right place. In particular it is difficult to schedule sufficient staff at short notice. As a result services are still being disrupted.
Southeastern said its services would start at the usual time on Tuesday, but most other operators warned of later start times.
Govia Thameslink said its services would start between 07:00 and 08:00. After that the operator aimed to offer a full timetable.
Northern, LNER, CrossCountry and South Western Railway also said there would be some impact on services at the start of the day.
GWR and East Midlands Railway said they would also start services later, and run a slightly reduced timetable during Tuesday.
Negotiations
The suspension of the strikes is significant, as it is the first time in the RMT's long-running dispute that a strike has been called off to pave the way for further talks.
The RMT union said on Friday it had called off the strikes after "the promise of an offer" on pay from the rail operating companies, and said it would enter "intensive negotiations" with the firms and Network Rail.
However, rail employers and the government said their position had not changed.
They have insisted that an improved pay offer depended on the union agreeing to reforms, particularly around how maintenance teams operate.
Network Rail has pressed ahead with a formal consultation that would allow it to make these reforms with or without RMT agreement.
That formal consultation process has been paused to allow for talks with the unions. If there is no agreement the consultation will resume on 3 December.