I have raised this with my local MP Jeremy Hunt who raised this with Dan Tomlinson MP who is exchequer secretary to the treasury and received the response attached (see photo). I responded to Jeremy with the below (aside from Iran war) but it would be useful for this to be raised with your MP also and I can share a template over the coming days.

I wholeheartedly disagree with the explanation! It is wrong for Dan to suggest that those on National Living Wage would not benefit, because if they travel using the train for work, they would (or could). Regarding the self employed, many operate as home based and can already claim transport costs for work as allowable (and non taxable) expense!

Salary sacrifice on a car doesn’t benefit those who can’t drive, nor those in London (or other major cities) who are unable to drive to work. I do not believe the salary sacrifice for cars should be removed nor pitted against each other, but I am highlighting this for the absurdity of his argument. 
Train season tickets would achieve more Government aims and ‘freezing fares’ is not meaningful especially as Dan has acknowledged 14% of spending is transport - with growth stagnating, this percentage will continue!

We cannot adopt this siloed approach to policy. After all, those who don’t have children still pay to run schools. Non-drivers still contribute to the roads. Non-claimants pay for benefits. Those without bus routes (or ones that are not useful to them) still support the system.

It is the aim of many local governments to reduce congestion and part of this would be utilising public transport. 

We should all be trying to reduce emissions and if more journeys were made using public transport, we will collectively make a difference. Rail costs in the UK are significantly higher than EU average (reportedly 2.5 times higher). As mentioned in previous correspondence, travel costs are a significant barrier in attending the office and by removing this barrier you are encouraging them to spend near the office which in turn supports the economy. This could provide untapped GDP growth. 

With the huge unemployment rates we should be doing all we can to support our workers as they (we) are propping up the economy.

Separately, given the change in outlook due to the Iran war, this should be given greater priority as this could make a meaningful difference to us all!