RT isn't really private; it's a non-profit funded by the Russian state: https://en.wikipedia.org/wiki/RT_(TV_network)#Foundation

Am I mistaken in understanding that BBC is similarly tied to the UK government?

The BBC is funded by a government-mandated tax, but has editorial independence. RT is explicitly a propaganda organ; its editor in chief has said as much. It's also aimed at foreign markets. It's more similar to VOA than the BBC.

Indeed, the BBC are of course totally editorially independent of the people who decide whether they continue to exist and at what scale. Also, I have a bridge in Westminster to sell you. (It's fairly well known here that they tend to be a mouthpiece of the Establishment and whichever party's currently in power.)

No it isn't. They are arguably currently at odds with the Conservative government over a range of issues. Do you know how strict the BBC's editorial guidelines are and the procedures they have in place to try and ensure impartiality?

BBC is independent from entity which gives it money to pay salaries and rent. Do you seriously believe that? Of course you are totally dependent on whoever is funding you.

RT specifically, but this type of media package was sold to a large number of media outlets, public and private.

Twitter itself is public and has become 'the medium' for much information.