The Labour mayoral candidate, Sadiq Khan, says keeping fares increases at 0% will cost £450m over four years, but TfL says the real cost will be £1.9bn, because Crossrail will bring in more passengers - and freezing fares means it won't benefit from inflation-linked fare rises.
In a briefing document, seen by BBC London, TfL says its £1.9bn figure "takes into account increasing ridership over the Business Plan (passenger numbers are rising by 5 per cent every year) and there will be new fares revenue from Crossrail when it opens in 2018/19".
An official said the Labour calculation did not include those factors.
TfL has an annual turnover of £11.5bn. It will lose £2.8bn in government revenue by 2020/21.
It is planning to raise £3.4bn by 2020/21 through being more commercial - that means selling and renting property and having more advertising.
And on top of that, it's planning to find £16bn in efficiencies by 2020/21. £4bn has been earmarked so far.
So as a would-be mayor who wants to freeze fares, your options are limited.
You can make efficiency savings, raise more commercial revenue, or opt for the far more politically unsavoury options of reducing the services TfL is running. Or you could reduce the investment in new infrastructure. Or you could go to central government and ask for money.
On top of that, TfL always lobbies extremely hard to keep control of its budget and its autonomy.
Fares policy isn't just about how much it'll cost commuters to get to work.
It suggests to voters how you'll handle finance.
It sets the tone on how you'll deal with TfL, and arguably it gives voters an insight into how you will run the administration.
To pay for the freeze, Sadiq Khan says that as mayor he would:
Speaking on the Sunday Politics, Sadiq Khan said: "Unlike any other candidate, I've actually got experience of being a minister in transport, and was the minister for Crossrail.
"My fares freeze is fully funded. We're going to make sure we make the savings this mayor hasn't made, but we're also going to increase revenue streams."
Tony Travers from the London School of Economics said: "The truth is that TfL has never felt austerity like much of the public sector - certainly nothing like the London boroughs. They have very substantial reserves that have been very substantial for years now.
"So if you ask the simple question 'could they stand a fares freeze?', the answer is yes. Would that mean, on the other hand, there was less money going into the system against which TfL could have borrowed in order for example to build the Bakerloo line extension? Well, that money wouldn't be there. So there will be less money in the system. And of course more crowding if fares don't go up."
The Conservative candidate Zac Goldsmith has not yet said what he intends to do with fares.
Transport for London (TfL) says Labour's costing of its fares freeze is wrong and doesn't take into account the impact Crossrail will have on passenger numbers.