Rail passengers have been warned that a strike by rail workers could disrupt services amid the bank holiday weekend rush, when transport networks are expected to be packed with holidaymakers.

Members of the Rail, Maritime and Transport (RMT) union at the operator CrossCountry are taking industrial action on Saturday 23 August and bank holiday Monday over pay and conditions.

The company – whose network centred around Birmingham runs to cities across Great Britain from Aberdeen in the north to Cornwall in the south – said it would offer a reduced timetable over the weekend, with no services on Saturday, and cancellations expected across all routes on Sunday.

It comes as Visit England has reported that more than 11 million Britons are definitely planning an overnight trip in the UK over the bank holiday break in England and Wales, which would mark an increase on the same weekend a year earlier.

CrossCountry is advising passengers not to travel on Saturday but to travel on either side of the weekend instead, or to claim a full refund.

The train operator said a “very limited” service would operate on Monday between 8am and 6pm, and advised passengers to check their journeys before departing.

Further journey details will be available on CrossCountry’s website in the coming days but it said there would be no service between Birmingham, Reading and the south coast, and no service between Leicester, Cambridge and Stansted airport. Only very limited services will run to south-west England and north of York.

Planned engineering work in the West Midlands is also expected to have an impact on the CrossCountry services that are running, meaning some journeys will take longer.

Shiona Rolfe, the managing director of CrossCountry, which is owned by Arriva UK Trains, said: “It is hugely disappointing to not operate any services on Saturday, knowing the inevitable disruption to many of our passengers’ journeys over the bank holiday weekend. We are committed to reaching an agreement with the RMT and remain available to continue talks.”

An RMT spokesperson said: “Our members have voted strongly in favour of industrial action, and we are seeking further talks with management to bring about a negotiated settlement.”

In June, RMT members at CrossCountry began an overtime ban and also started to refuse to work on rest days, as they accused the company of declining to negotiate over increased pay for overtime and rest day working, which it said went against previously agreed commitments.

The coach operator National Express said it was increasing capacity on its intercity services over the bank holiday weekend in response to industrial action, adding 9,000 extra seats on routes including Birmingham, Cardiff, London, Leeds, Manchester and Nottingham.

Motorists have been warned they could face long delays on the roads over the weekend, when 18m car journeys are expected to take place, while the RAC has advised travellers to set off as early as possible.

The heaviest congestion is expected in the south-east and south-west of England, while delays are expected on the M20 in Kent for drivers crossing the Channel from Dover or Folkestone.