Passengers queue for a reduced Gatwick Express service during the Southern railway strike at Victoria station in London, Britain December 13, 2016. REUTERS/Neil Hall

By Sarah Young

LONDON (Reuters) - British Prime Minister Theresa May condemned as "appalling" a rail strike that left hundreds of thousands of London commuters facing a second day of travel chaos on Wednesday.

Speaking in parliament, she urged the two sides to find a solution to avoid prolonging Britain's worst rail disruption for two decades.

Passengers trying to get to London from the southeast struggled to get to work as drivers on Southern Rail - part of the country's biggest rail franchise - continued a 48-hour stoppage over a dispute about whose job it should be to open and close the train doors.

May called for an end to the action as Southern and the drivers' union Aslef met for talks at the conciliation service Acas before more stoppages planned for Friday and in January.

"This is an appalling strike," she said. "We've seen driver-only operated trains on rail networks in the UK for decades. I hope that the talks at Acas are going to lead to an end to this strike."

"There is only one body responsible for the current strike, that is Aslef," she added.

Wednesday's talks have not yet involved the other main rail union, the RMT, which represents conductors, and is also involved in the dispute. It is planning strikes on the Southern network next week.

Southern, run by Govia Thameslink Railway (GTR), a joint venture owned by London-listed Go-Ahead and France's Keolis, told passengers not to try to travel during the strike.

Commentators said this week's strikes would have the biggest impact since action by signal workers in the mid-1990s.

They follow a series of stoppages on Southern this year which have caused misery for commuters. Some of them say they have even lost their jobs because they could not get to work on time.

Southern said in a statement it hoped the talks with Aslef would be productive, and added that it had asked to speak to the RMT at Acas later on Wednesday, to try to end the dispute.

Parent company Go-Ahead, which has apologized for the troubles on Southern, is due to provide investors with a trading update on Thursday.

The strike action on Southern is not a major concern for Go-Ahead investors due to the terms of the contract between the rail operator and the government which mean the latter must take the hit for revenues lost to strike action.

(Additional reporting by Michael Holden, editing by Stephen Addison)