LONDON--London braced for a 48-hour strike by subway workers starting Tuesday evening which threatens to cause significant travel disruption for millions of commuters and tourists who rely on the world's oldest underground railway.

Prime Minister David Cameron called for Bob Crow, the leader of the National Union of Rail, Maritime and Transport Workers, or RMT, to call off the strike, saying it was "plain wrong," Cameron's spokesman said.

The RMT and the smaller Transport Salaried Staffs' Association have marshaled their members to stop work for 48 hours from 2100 GMT Tuesday to protest against London Underground's plans to cut about 750 jobs as part of a drive to automate ticket sales. A second 48-hour stoppage is planned to start at the same time next Tuesday.

The Tube, as the London Underground subway network is known locally, carried more than 1.2 billion customers in the last fiscal year, to April 2013, with more than 4.5 million on the busiest days.

Boris Johnson, the mayor of London, pleaded with Mr. Crow to call off the strike when the union boss phoned in to his regular live radio show to explain why the industrial action was being taken.

Mr. Crow said he would suspend the industrial action if London Underground withdrew its notice to cut jobs. In response, the mayor said there would be no compulsory layoffs as part of the modernization program, and more than 1,000 London Underground staff had already expressed an interest in taking voluntary redundancy.

Neither made any headway. As the initially civil exchange became more hostile, Mr. Johnson accused the union of knowing it couldn't stop the network's modernization program but striking anyway as a show of strength to its membership.

"Unfortunately we are going to have to go through it [the strike]," Mr. Johnson concluded. "I urge Mr. Crow to call off this strike which will achieve absolutely nothing. Do the right thing for yourself, your members, for London: get round the table...and let's take this thing forward."

The mayor said the network would do its utmost to keep services running, and extra bus services are planned. During a previous RMT London Underground strike in 2010 some trains did run, but they were overcrowded and passengers faced long delays. Above ground, trains and buses were also much busier than usual, while some commuters chose to cycle to work and others worked from home.

In a statement ahead of the strike, London Underground said: "Please try to complete your journey as early as possible on Tuesday evening. The strike will disrupt services throughout all of Wednesday and Thursday. Services will not return to normal until Friday 7 February."

London Underground announced in November that it planned to close ticket offices at subway stations to reflect the growing trend of customers buying tickets from machines or using the oyster card, a smart card that can be refilled on ticket machines or online. Less than 3% of journeys now involve a visit to a ticket office, it said.

Rather than working in ticket offices behind glass windows, staff would instead be based in the station ticket halls, at gates and on platforms and would be equipped with mobile technology so they can manage stations, it said.

Those changes, coupled with plans to run a 24-hour service on certain lines of the network on weekends from 2015, would involve the net reduction of about 750 staff, it said. London Underground employs about 18,000 staff, including about 5,500 station workers, it said.

The unions say the plans will turn some stops into "ghost stations" with no staff on duty, making passengers vulnerable to crime. It has also warned that station supervisors will be left to oversee multiple stations meaning they may not be on site to help in an emergency.

Write to Nicholas Winning at nick.winning@wsj.com

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