Rail services are set to increase later this month as part of the gradual easing of the lockdown.
Sources said there will be a gradual increase from May 18.
Rail unions have been involved in talks about the safety of workers and passengers when more trains run.
Some areas might see a return of similar services to a Saturday.
Union leaders stressed they want to make sure their members’ safety is protected, with one saying lifting the lockdown was “fraught with danger”.
Mick Cash, general secretary of the Rail, Maritime and Transport union said: “There is a headlong dash to lift the lockdown on our transport services for May 18 and it is fraught with danger for both passengers and staff alike.
“To maintain the Government’s own social distancing guidance would mean huge logistical and staffing input to manage passenger flows onto trains and it is imperative that all staff involved in this process are properly protected.
“RMT will not compromise on the health, safety and livelihoods of our members and we will not agree to anything that fails to put the safety of staff and passengers first.
“If that means advising our members not to work under conditions that are unsafe and in breach of the government’s own guidelines then that is exactly what we will do.”
Mick Whelan, general secretary of the train drivers union Aslef said: “We have worked with the Government and all stakeholders in the rail industry throughout this crisis to ensure that key workers get to work, and food and medical supplies are moved around the country.
“We want to help Britain return to what we knew as normal before the pandemic, and have agreed with the Department for Transport that we will increase the number of services when and where it is safe for passengers and for staff.”
A Department for Transport spokesman said: “We are examining a range of options on how transport can respond to support the recovery in a timely way when the time comes and it is safe to do so.
“We continue to prepare for any scenario we might be asked to support.”
A spokesman for the Rail Delivery Group, which represents train operators and Network Rail, said: “When Government decides the time is right, the railway will respond to support the nation during the next phase of the coronavirus response, as it has done throughout the lockdown.
“Our priority will continue to be the safety of our staff and passengers and we will work closely with Government and unions to run trains safely while supporting the economy and the public’s health.”