Poppagator, just because land is owned by public bodies, and in that sense is publicly-owned, doesn't mean that the public has free rights of access to that land and can do what it likes. Public bodies have the same rights as private corporations and individuals to control what access is allowed to the public and what activities are permitted. These rights are subject to the law in general and the bodies' statutory functions and authority in particular.

In the UK, a right of way is just that - a right to pass over land. It does not grant any other rights, including the right to stop and busk.

TfL has the right to control, and indeed prevent, busking on the London Underground. They could have banned it completely, but instead have a fairly enlightened policy which maintains musical standards and avoids disputes over pitches and annoyance to travellers. I can't comment on the rights and wrongs of this particular case, but even if the original basis for the thread had not been shown to be wrong, TfL are entitled to decide who and who not may busk on their premises, and even entitled to ban banjos is they wished to do so.

I would be surprised if that is any different in the US. If the public has unfettered access to the public transportation system, then how can the transport authorities charge a fare? Where there is a difference between the UK and the US is that we don't have your First Amendment rights which (if I understand the arguments in the Seattle Folk Life thread ) would prevent a public body from exercising the same control over buskers.