Members of the Aslef union walked out for 48 hours at midnight. A further 24-hour strike is set for Friday.

About 300,000 passengers usually travel on 2,242 Southern services every weekday. There will be no trains on any route and people are being warned not to travel.

The government said it may consider banning strikes on the railways.

Transport secretary Chris Grayling dubbed the action as a “deliberate act of militancy” and said he would examine possible changes in legislation “very carefully.”

Aslef and the Rail, Maritime and Transport (RMT) union said ministers had prevented Southern from negotiating properly.

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How bad have Southern rail services got?

Analysis by Chris Mason, BBC Political Correspondent

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Ministers say they have no legal power to halt this dispute but are pointedly publicly entertaining the idea of changing the law, albeit without offering any detail about how they might do this.

Chris Grayling told the BBC he would look at all the options when this strike was over, and while he wasn’t “ruling anything in” he wasn’t “ruling anything out” either.

The general secretary of the Aslef trade union, Mick Whelan, said the strike wasn’t politically motivated – but a response to what he called “ill conceived” changes “fraught with danger”.

Passengers have suffered months of disruption in the dispute, which is about whose job it should be to open and close the train doors, but this is the first strike by Aslef drivers.

It has closed most Southern routes although there is a limited Gatwick Express service to and from London Victoria.

London Mayor Sadiq Khan said Southern rail passengers had been “abandoned by the government”.