Libertarianism, if it be the promotion of individual liberty and individual responsibility, is neither left nor right. In the British context it is neither Conservative nor Labour. It is not, essentially, about a political form at all but rather the removal of 'politics', of controlling power and coercion, in the life of the individual. (If only the directors of the now almost deceased Libertarian Party had embraced that!)
Insofar as the Conservative Party has its roots, and demonstrates its adherence to those roots, in the old aristocracy that ruled and controlled day to day life, it is anti libertarian. However in the 21st Century, and in much of the 20th, it has been Labour that has been the party of centralised control and intervention in the daily lives of the people.
In fact the Conservatives of Thatcher would probably have had more in common with the Whigs of old, and the Labour control-freaks and micro managers more with the old control-centred Tories of two centuries ago.
For the last 50 years or so both parties have indeed been different flavour of the same stuff. Today even, Cameron is less conservative than Blair was when he came to 'power', which he did by appealing to the popularity of conservative sentiment in the voters more effectively than the 'depleted-Conservatives' did in 1997.
During the 20 or so years before Labour's return under Blair, and for some years after, freedom did regain that bit of a breathing space because individuals within the Conservative Party had seen the individualistic beliefs they held dear, as well as simple, survivable reality, being dangerously eroded under old Labour. The changes in sentiment the Conservatives introduced after being elected in 1979 were not eradicated by New Labour until the collective public memory of why the Conservatives had been voted in had been obfuscated, re-written, and had faded. To repeat, the policies did not hit the buffers, the Party did after it abandoned those policies.
And now the forces that rolled back centralised control have been largely contained and neutralised and that breathing space for freedom is closing up very, very fast. The spirit of centralised controlled as exemplified previously by the USSR rides again with a whole new dimension on totalitarian terror from a different quarter; out of the Middle East and Middle Ages.
Politics is a shifting game and will always be open to deception. It is inherently dishonest being as it is, about power, and the manipulation, coercion and control of others.
Further, all too often one sees political debate revelling in tricks of thought and speech rather than with substance. It's about winning rather than addressing the truth.
However it would seem there would be more hope to promote libertarian agendas within the Conservative Party than within Labour. There is a spirit that has flourished from time to time amongst some of those in the Conservative Party that is far more libertarian than could ever be expected in Labour, unless that party were to go beyond the robust addressing of reality that occurred during Blair's first few years in power, and that probably actually came from Alistair Campbell, whatever his world view, and Labour actually seriously committed itself to the truth.
Self reliance, responsibility for one's self and actions, is far more in keeping with those who have built the nation rather than those who have used it to fund themselves, their programmes and their Utopian hopes