Jeremy Corbyn has said he would be prepared to join the striking Southern rail workers on a picket line, blaming the government for protecting the company despite its poor performance.

A day after Transport for London (TfL) station staff went on strike across London’s tube network, Southern train services were cancelled on Tuesday, as well as on Wednesday and Friday, in the latest strikes on the commuter rail network. These are the first walkouts of the new year in a long-running dispute at Southern over whether drivers should operate train doors.

“I think many people trying to commute in from Brighton are utterly fed up with Southern rail and the way it has behaved,” Corbyn said.

Asked if he would join striking drivers and guards on picket lines, the Labour leader told BBC Radio 4’s Today programme: “Yes I would, because I think Southern rail have behaved in a terrible manner and the government seems to be more interested in protecting Southern rail despite its appalling service and shortage of trains, overcrowding, and continues allowing them to run the franchise.

“I would want that franchise brought back into public ownership because we provide the rails and the trains and they make the profits.”

Corbyn later told Sky News he was not planning on joining a picket line on Tuesday, because of a shadow cabinet meeting and his planned speech on Brexit in Peterborough later in the afternoon. “I’m not going to a picket line today, but what I’m saying to the government is get together with those who travel on the trains, who work on the trains, to get a solution,” he said.

Labour’s mayor of London, Sadiq Khan, condemned the tube strikes on Monday, but the Labour leader said he understood the concerns about ticket office closures that had prompted them.

Khan had called the strikes “completely unnecessary” and said he had already announced the creation of 600 jobs across the network by the end of the year, as a step towards replacing those cut by the former mayor Boris Johnson.

Corbyn said: “I still believe that the lack of ticket offices, certainly at the major interchanges, is a problem. What should have happened is the continuation of the negotiations and another offer made by TfL, and now we’ve had a one-day strike and the union has shown its determination to pursue this.

“I would hope there will now be agreement on this, because it’s not a strike about wages, it’s a strike about some jobs, though TfL say the number is minimal, it’s about services to the public and I hope there will be a new offer made by TfL and I urge them to resume negotiations as soon as possible.”

About 2,500 British Airways crew are also set to strike on Tuesday and Wednesday, although the airline said only a small number of flights from Heathrow would be affected.