It would be unlawful for any restriction to apply to public transport specifically.
If they are asking people to make only "essential" journeys by any mode then fair enough (notwithstanding any such arguments over whether such measures are proportionate; that's a whole new topic) but the idea that non-car owners can be subject to additional restrictions compared to car owners is absurd and the fact that anyone is trying to suggest this is absolutely abhorrent.
Anyone who is responsible for this disparity has extremely questionable morals; I'd like to have an argument with them (and it would bes the full argument, not the 5 minute argument
).
Even the disgrace that is Transport for Wales were not actually restricting people at any point, as they
divulged in a response to an FOI request. It's just weasel words that some people/organisations of dubious character say to deter people from travelling. While it is disgraceful that these views are expressed as official 'guidance', people have the right to ignore any advice that appears to be imposing unlawful disparities in freedoms between those who rely on public transport and those that don't.
Any attempt to impose unlawful restrictions by authoritarian regimes that promote the interests of wealthier individuals, at the expense of those who use public transport, must be bitterly and robustly opposed.