No. It's a non profit, licence funded public organisation. Slightly differnt but the difference matters.
The licence fee may be considered a "tax", but it goes straight to the BBCthe BBC. It doesn't go into the general tax pool.
It is explicitly separate from government and while it's impossible to keep them completely isolated from each other, this separation is taken very seriously. The BBC has no qualms about upsetting the government, and any government that tries to exert pressure will be very unpopular.