Liberals are not libertarians. They believe in pluralist/multilateral politics, well regulated but ultimately free markets, they do not dictate social mores, in theory (though not in practice) they believe in evidence-based policy-making.
Traditional left-wingery has been far more authoritarian - punishing the rich, giving money to the poor. There is a much greater tradition of "solidarity" in various forms - unions being the obvious examples. They are often quite socially small-c conservative. They believe in controlling markets (not just regulating them).
Toryism (especially One-Nation) is rooted in a respect for institutions and traditions - with change coming through evolution rather than revolution. There is a slightly authoritarian streak here too but with a very different flavour - they prefer to call it "paternalist". They believe that family action is better than social action, and that social action is better than state action. They believe in "quiet" patriotism, and very much in Burke's "litte platoons".
Cameron and Clegg are both essentially Liberal Tories or Conservative Liberal - with Clegg usually more liberal, and Cameron more Tory, obviously.
Thatcherism is a pretty new form of Conservatism. It usually, but not always, blends well with traditional Tory.