No, is the short answer. The media’s power is vastly overestimated both by politicians and, of course, journalists, but also by ideologues from all sides who blame the defeat of their hopes on the power of the Tory press, if they are left wing, or BBC bias if they are on the right.
A few seconds thought should convince you of the folly of the notion. The BBC has a pro-European bias, but that has not stopped the British, or more specifically the English, being Eurosceptic. The media cannot run too far away from their readers and viewers or their readers or viewers will run from them.
If that argument does not suffice, consider Lord Beaverbrook and Lord Rothermere’s campaign in the early 1930s to insist that Baldwin commit the Tories to Empire free trade. Everyone remembers Baldwin’s put down – “What the proprietorship of these papers is aiming at is power without responsibility, the prerogative of the harlot down the ages.” (Kipling came up with the line for him, incidentally.)