It's a bit of legal fiction really. A government with a sufficient majority that felt like taking on one of the more respected/loved institutions in the UK could absolutely abolish the BBC if it wanted to, and can set the budget of the BBC and set the license fee. The current conservative government forced the BBC to cut its budget while taking on additional costs, e.g. the over 75s free license, and the cost of running the World Service (previously funded by the Foreign Office),
In reality Parliament cannot create any institution that it cannot also eliminate or change if it wanted to. It's why QANGO stands for "Quasi-Automimous Non Governmental Organisation", and isn't "ANGO". These sorts of arrangements are just there to put the organisation at arms length and make it clearer when the government or Parliament are exerting their authority (which they have done many times with the BBC, such as forcing out the director general).
The quasi-independent model is actually pretty common in many countries, including as someone else mentioned the German public service broadcaster.
In reality Parliament cannot create any institution that it cannot also eliminate or change if it wanted to. It's why QANGO stands for "Quasi-Automimous Non Governmental Organisation", and isn't "ANGO". These sorts of arrangements are just there to put the organisation at arms length and make it clearer when the government or Parliament are exerting their authority (which they have done many times with the BBC, such as forcing out the director general).
The quasi-independent model is actually pretty common in many countries, including as someone else mentioned the German public service broadcaster.