The Spectator is currently owned by David and Frederick Barclay, who own the Daily Telegraph (and the Sunday Telegraph), and held through the UK holding company, Press Acquisitions Limited, wholly owned by the Barclays,
through Press Holdings (registered in Jersey by the Barclays).
They also own May Corporation Ltd (Jersey-registered), a partner in Press Acquisitions Ltd.

I haven't checked on other interests of the Barclays.