I think that's some slightly naive calculations.
https://publications.parliament.uk/pa/cm5801/cmselect/cmtreasy/664/66408.htm is from a presentation to Parliament about tax and includes:
You have to take into account that people will change their behaviour in relation to taxation, so it won't be a simple arithmetic increase. Dropping the 50p tax rate down to 45p was estimated to have only cost £360m over 5 years as people no longer structured their affairs to avoid it.
Thanks, I knew the numbers would likely be off (as who's going to try and avoid a 5% tax rate, but once it gets to above 25% people are likely to see benefits from avoiding it where they can) but was trying to get a starting set of numbers - even if they were likely to be naive.
Assuming that the +1% was applied to both the basic and higher rate then it looks like it'll add £6.8bn, so increasing it to +3% on both would potentially get you something like £20bn maybe a bit less due to people trying to avoid more the higher the rate (3*6.8=20.4), so probably isn't far off the mark to get a decent amount of money to give all rail travel for free and still be able to invest something and still have a bit left over.
(I suspect that's why Labour are looking at council tax costs to rise extra money. As the value of the house stay the same, so unless someone abandons it they'll still get the money and if someone sells up to avoid the higher tax they get extra income from stamp duty from the purchaser.
If that's the case, could a similar property tax (i.e. on properties worth over £500,000) be a better way to fund public transport, not least because you could adjust it based on the cost of providing public transport to a given population size (so higher rates for sparsely populated areas, but not impacting those who are on low paid jobs in such areas).
For example based on the cost to carry 5,000 public transport passenger movements a day on public transport capacity for each 100,000 people. Meaning if a town of 50,000 had no-one using buses the tax would be effectively be based on transport costs for those 5,000 movements were undertaken by taxis and so they would have to pay more in taxes than if public transport was used well enough that it was all on £2 bus fares (or the historical train ticket prices).
Which would mean the population would want decent frequency public transport so more people used it, you may even get people using public transport to try and reduce their tax bill!
If you ended up with people selling their rural/coastal second homes then there's many who would think that wouldn't necessarily be a bad thing.