I'm quite a fan of Hayek, The Road To Serfdom is an excellent critique of socialism and its tendancies to totalitarianism (some of which is scarily relevent today with the managerial style of politics).
I think its wrong to put Hayek and Keynes in opposition, Keynes read The Road To Serfdom and praised it highly. I think its Keyenes's successors who took parts of his economics and took them to extremes and didn't understand that they were meant for the depression of the 30s specifically.
The same with some people who follow Hayek or Adam Smith, they take sections and ignore other parts (like the fact that markets fail, or that effective competition is not always available or that a minimum income can be provided in a wealthy society like ours)

I'd also describe Friedman as a Liberal. Reading him on things like school vouchers you get a sense of deep concern for individual rights and opportunity and social justice. He is quite definitely an individualist because individual freedom is the best way to better living standards and prosperity ofor the many.

Thatcher to me seems to have been an anti-socialist who took some liberal views but didn't understand the central tenet of the limit of power (or chose to ignore it if you're being less charitable).

The IEA are very interesting, and I agree with much that they say. Perhaps if the Liberal Party had been stronger they'd have gone to them rather than the Tories...
Likewise, the Adam Smith Institute has some very interesting things to say, although they tend to believe that liberal economics alone can provide a solution to all our problems which for me is taking things too far.