On Eurostar, I don't know the precise position without digging but you need to start with the inter-governmental treaty (Canterbury?) and how it is affected by the subsequent nth Railway Packages (union law, but may not trump a treaty) and finally the 2020 Withdrawal Agreement and any subsequent inter-govermental working group stuff (international treaty so overrides previous law) to understand precisely what governments can and can't tell Eurostar to do legally and how Getlink goes about allocating paths, again legally so that it cannot be challenged in court.
The essence is that before we left it was liberalised in the same way as other intra-EU rail traffic albeit with a different legal basis. I assume that the Withdrawal Agreement etc preserved that status but I don't know for sure.
From the way Getlink are encouraging competing users for the free paths that were previously defined in the treaties it is clearly up to them and the legal framework, not national governments.
On the flights point, check how aviation law works, in particular bilateral air services agreements and the differences for EU member states. We left EU open skies and now have a bilateral treaty with the UE which is supposedly similar. Renegotiating that is EU level and therefore would first need a common position by all heads of government for the EU to negotiate with us. Expect nasty surprises such as Ryan or Wizz pressurising Ireland, Hungary or somewhere else to put a spanner in the works.
This stuff is horribly horribly difficult and it's best when politicians are kept out of it (by previously agreeing that they won't interfere, which takes us back to the competition-based approach for which the UK pushed for so long).
