Following the power cut, an update from National Rail at 18:13 BST said the CrossCountry service between Peterborough, Cambridge and Stansted Airport will be running on Sunday evening.
The update also said the operator had been able to resume operating an hourly train service from Birmingham New Street to Leicester and Derby.
Transport Secretary Heidi Alexander said: “Following earlier disruption on CrossCountry services, I am pleased to hear some trains are set to run tonight, and a full timetable expected to resume tomorrow.
“While passengers should continue to check their journeys before they travel, I’d like to thank engineers who are working tirelessly to minimise disruption as much as possible.
“We are setting up Great British Railways and nationalising services, including Cross Country next year, to end decades of fragmentation and vulnerability on our network. We are determined to give passengers the reliability they deserve.”
The National Union of Rail, Maritime and Transport Workers (RMT) has called for a review of railway operational control centres following the disruption, “to ensure they remain unaffected by power outages.”
RMT general secretary Eddie Dempsey said passengers and rail workers should not have to face another week of “travel chaos” because of unreliable back-up systems.
