While the BBC is in charge of collecting it, and it is largely (but not exclusively) spent on the BBC, the TV licence is imposed by and paid into the government's funds. The government then "grants" the money back to the BBC.

> The revenue and associated expenditure [...] are those flows of funds which are handled on behalf of the Consolidated Fund and where the BBC acts as agent rather than as principal

https://www.tvlicensing.co.uk/ss/Satellite?blobcol=urldata&b...

The Office for National Statistics also classifies it as a tax: https://publications.parliament.uk/pa/ld200506/ldselect/ldbb...