TfL is not fully self-funded, or even close to it. It derived 47% of its funding from fares in 2017/2018. https://tfl.gov.uk/corporate/about-tfl/how-we-work/how-we-ar.... In fact, it's facing a large (close to £1 bn) deficit this year due to falling passenger numbers.

Thanks for the correction. I think the 47% figure is misleading in this sense though, I mean to refer to the running and maintenance costs of the public transport service, but in fact of course TfL does various other things, including maintenance of the roads and contributions to large capital investments like Crossrail which will always mean public grants.