Theresa May has now signed a letter to trigger Article 50, the start of the official process to leave the EU.
More Tube Strikes
Two more 24 hour Tube strikes have been announced, which will lead to disruption for almost a whole working week.
Members of three unions plan to walk out for 24 hours from the evenings of August 25 and 27, threatening to disrupt services for days in the run up to the August Bank Holiday weekend.
Two strikes have already been held in the past month over plans to start new night Tube services from September 12.
Unions are unhappy over pay and shift arrangements for the new services, which are due to be launched at weekends.
Talks at the conciliation service Acas have failed to break the deadlock, although the two sides are due to meet again tomorrow.
RMT general secretary Mick Cash said: "Our members the length and breadth of London Underground have made it clear that they are determined to protect their work/life balance and not fall into a trap where they will be forced to wreck their home lives in order to comply with the 'rosters from hell' which have been drawn up to plug the staffing gaps in the night Tube plans.
"Staff are angry that their grievances are being ignored and dismissed by both the Mayor and his officials and that there has been no substantial move as of today from London Underground to make progress towards a negotiated settlement.
"That is why we have no option but to strike again. It is ridiculous that the job cuts programme for fleet, engineering and station staff is also still being bulldozed through against this background."
RMT members will strike from 9pm on the two evenings, while members of the TSSA and Unite will take action from 6.30pm.
The drivers' union Aslef made no announcement about strikes.
TSSA general secretary Manuel Cortes said: "It is now time for the mayor to start getting his hands dirty and get down to serious direct negotiations to avoid a week of disruption on the Tube. He should stop playing Pontius Pilate.
"Our members will not accept top down change being imposed on them when it comes to changes in their work-life balance.
"We accept the night Tube, but only with detailed agreement on how it will operate safely for both passengers and staff."
Steve Griffiths, LU's chief operating officer, called on unions to engage in "calm and realistic" talks.
He accused the RMT of making further demands for "unaffordable" pay rises and hiring more staff, as well as reversing the modernisation of customer services in Tube stations.
"They expect our customers to pick up a bill running into hundreds of millions of pounds for this through higher fares or by forcing us to cut back investment to improve Tube services in a rapidly growing city. No responsible management can give in to such demands."
Mr Griffiths said LU had put forward a "very fair" revised offer, guaranteeing staff the same number of weekends off as they have today.
Unite regional officer Hugh Roberts said: "London Underground's vague assurances over work/life balance and unsocial shifts ring hollow and don't go far enough in giving our members the security they need to plan their home life over the long-term.
"If not enough people sign up for night shifts what happens then? London Underground has made it clear that people will effectively be forced to work with its insistence that staff are contracted to work 24/7.
"It is a move that tears up existing contracts and runs contrary to the actions of any reasonable employer wanting to change shift patterns."
A spokesman for Mayor of London Boris Johnson said: "The union leadership appear hell bent on strike action and the Mayor is dismayed at their continued failure to put what is a fair, sensible and generous offer on the table to their members.
"Tube workers are being offered an above inflation pay rise, cash bonuses and a commitment that no one will be asked to work more hours than they do today. The mayor continues to call for the unions to present that offer to their memberships and put an end to the completely unnecessary threat of industrial action."
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