Industry body the Rail Delivery Group (RDG) said timetables will be increased to around 90% of pre-coronavirus pandemic levels.
This will mean additional and longer trains on many routes, particularly at peak times.
Anthony Smith, chief executive of passenger watchdog Transport Focus, said existing and returning passengers will welcome the capacity increase as “many will now have more choice and a better chance of maintaining social distancing”.
He added: “The rail industry must focus on maintaining good performance so that passengers can travel with confidence.
"Disruption and any crowding from this will be especially unwelcome and has the potential to damage trust in the railway.
“The industry also needs to keep an eye on passengers numbers, and checking if gaps in services are causing problems.”
A survey of 2,000 public transport users by Transport Focus conducted last month suggested that 77% of train passengers were satisfied with the ability to keep a safe distance from others.
The research also indicated that 50% were satisfied with the ease of finding out how busy a train service would be before travelling, and 69% were satisfied with the number of people wearing face coverings.
It is mandatory to wear a face covering on public transport, apart for people with exemptions.
A recent study by the Rail Safety and Standards Board concluded that the risk of contracting Covid-19 on an average journey is below 0.01%.
LNER is adding 10 extra Anglo-Scottish services to its timetables from Monday, serving destinations such as Peterborough, Doncaster, York and Newcastle.
The operator will continue to require passengers to reserve a seat in advance of travel to support social distancing on board.
Managing director David Horne described LNER’s return to around 85% of its pre-Covid-19 timetable as “a significant step forward”.
He said: “We are seeing more people travelling on our trains and these extra services will ensure that we can maintain social distancing in the coming weeks.”
Southeastern is adding an extra 900 carriages and 50,000 seats to its weekday services from Monday, restoring timetables to 98% of normal levels.
This will include boosts to routes serving London St Pancras International, London Cannon Street, Dover Priory, Ramsgate and Gillingham.
Passengers checking departure boards at Southeastern stations or on its website will see red, amber or green indicators showing the available capacity of trains.
Latest figures from the Department for Transport show rail usage in Britain is at 31% of pre-pandemic levels.
Timetables were slashed in March as the virus led to a reduction in available railway workers and demand for travel.
But services were increased to around 80% of normal levels following uplifts in May and July.
ScotRail further increased services last month ahead of lessons resuming at Scottish schools.
Some operators are returning to normal refund rules on Monday after restrictions were eased due to the pandemic.
This means season ticket refunds will no longer be backdated up to 56 days from the last date of travel, and admin fees of up to £10 may return for refunds of single or return tickets.