https://www.gbnews.com/lifestyle/cars/weather-air-con-postpone-car-journeys-warning

It adds: “Give yourself the best chance of avoiding delays by checking road conditions if driving, or bus and train timetables, amending your travel plans if necessary.”

This has been echoed by the RAC, which explained that red extreme heat warnings are incredibly rare, and called on Britons to take them seriously.

Data from the organisation states that breakdown volumes are expected to be around 20 per cent higher today than what’s normal for a Monday in late June.

I literally just searched for it and trivially found them.

They’re specifically saying vehicles without air conditioning, while also discussing worsening road conditions, increased risk of breakdown, and a general need to limit travel.

They issue the warnings for trains and not cars because train rails expand in the heat, meaning service cancellation is more likely and deferring optional travel reduces stress on the system.
Any time there is stress on a transit system they advise people to skip using it if necessary.

Your position is not hard to understand. It’s just one-sided because you’re only considering the downsides of one method, and not considering what the same situation looks like for the other.