Article 1 of Protocol 1 of the ECHR covers exactly this, so the Supreme Court (and ECtHR if it came to that) would probably find in favour of Royal Mail if this were to be done without compensation.
If it were done by an Act of Parliament, no they wouldn’t. If that Act explicitly overrides external concerns, the Supreme Court must find in favour of the Act and the ECHR would have to find against it, which the UK Parliament is free to ignore, if it so chooses.
As I point out, this isn’t “free” because it can invite consequences from other parties. But that’s a different domain to law.
