Some years ago the BBC itself ordered a study by Nottingham University which did show that the BBC consistently was pro-whatever-party-was-in-Government, so not being pro a specific party but switching from one of the parties of the power duopoly in Britain to the other as they alternated in Government (funnilly enough giving very little airtime to the smaller leftwing-ecologist party and tons of airtime to smaller far-right parties like UKIP).
However that's about the News, not the rest.
Mind you the BBC also does in it's contents invariably beautify the view about certain slices of British Society and British History but that's the same as the 100% private content producers in the US also do, so it doesn't seem to be an explicitly "Public TV" thing.