As a political force, it is impossible to see how a Libertarian political philosophy could function within a party political system. For Libertarianism to emerge as political force, the party political system would need to break down first, where MPs did not belong to a Party, and just represented a constituency. This was the parliamentary political system in Britain before The Tories and Whigs became homogenous parties.
Libertarianism is incompatible with party politics, because a Libertarian sees themselves purely as an "I", an individual. They do not construct a notion of "We", and the idea of being a "We" is essentially to forming a party.
Party politics requires entering into a tribal "We" identity. This "We" constructs itself in opposition to "The Other". In other words, party politics requires identifying as part of a tribal "We" e.g. Labour, and thus loathing "The Other" e.g. Conservatives.
Libertarianism is not compatible with this becoming a "We". The Libertarian is an individual; and, therefore, becoming a "We Libertarians" is oxymoronic. Instead of being a tribal "We", Libertarianism is all about the individual being an individual. However, being part of politics requires losing individual identity to become part of a "We" e.g. "We" the Labour Party.
In essence, the construction of party politics prevents the emergence of Libertarian political philosophy. Party politics requires the coming together of "I"s to become "We"s, and a political philosophy that prioritises being an "I" above all else, and where being a "We" would be an oxymoron, prevents Libertarianism from emerging as a political force.
Despite the suggestion that the party political system is breaking down, this seems to be a rather premature prediction. The adversarial idea of "We" in battle with and the terrible other is still dominant in politics. This is not abating, but exacerbating, because the current parties in Britain are pitching themselves more against "The Other" e.g. Labour is condemning The Tories, more than it is creating a vision. What unites parties is the tribal mentality of being a "We", being Labour as opposed to Tory. It is this kind of think that Libertarianism just cannot do, because Libertarians don't want to be a "We", just an "I".