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Sadiq Khan was today accused of breaking his key election promise to freeze fares as it emerged hundreds of thousands of Londoners will miss out.

The Mayor admitted the freeze would not cover daily or weekly travelcards or contactless caps — used by half a million Londoners — claiming they were not under his control.

However, Transport for London confirmed it was for the Mayor to set all fares and then to negotiate with the Department for Transport about which of them covered the cost.

Mr Khan had promised in his election manifesto that Londoners “won’t pay a penny more for their travel in 2020 than they do today”. But he admitted today only single tickets and pay as you go would be frozen, although up to 11 million passengers would benefit.

It came as TfL said it could now afford his four-year fares freeze without damaging investment in the capital’s transport infrastructure.

The transport body claimed the pledge would now cost £640 million — substantially lower than the £1.9 billion figure it gave during the election campaign, which included the cost of freezing travelcards — and could be funded by major cost-cutting. This would include organisational restructuring, cuts to agency staff and a recruitment freeze, as well as a pay freeze for 70 senior staff and cuts to free travel perks for the families of high earners.

This would deliver the cash for the first two years, with TfL working on the remaining two, against a backdrop of it losing its central government grant.

Mr Khan’s announcement will come as a disappointment to some Londoners. Lib Dem Assembly member Caroline Pidgeon told him: “I think you have broken your fares promise today”.

Tory group leader Gareth Bacon said: “The Mayor’s flagship policy has been thrown out of the window. By raising travelcard prices by inflation and breaking his biggest promise he is turning his back on those who showed faith in him.” London government professor expert Tony Travers added: “Londoners will have formed the impression the commitment meant a freeze for all fares for four years. A freeze only affecting pay as you go fares is very different.”

The Labour Mayor’s pledge became a key battleground of the mayoral race with the Tories claiming it risked crippling TfL’s £2 billion infrastructure programme. TfL chief Mike Brown publicly defended the £1.9 billion figure, angering many in the Labour team.

The new mayor had claimed the move would cost £450 million over four years, and City Hall admitted today the £640 million figure was an estimate as the actual cost would depend on inflation and passenger numbers.

Mr Brown confirmed the modernisation of the network, including Tube upgrades, Crossrail 2 and more investment in cycling and the road network, would go ahead as planned.

TfL’s original £1.9 billion figure had differed so starkly from Labour’s because they used different inflation measures, it covered five rather than four years, passenger growth had been lower than forecast, and it included all fares at the request of Labour.