Since Labour toppled the once-mighty Liberal Party in the interwar period, we've had several other abortive attempts to transform the British political scene. In the 1970s it was the National Front, in the Eighties it was the SDP (of 'breaking the mould' fame) and the Green Party. Yet other than the long, slow march of the Liberals (and later, the SDP) to third-party status, the post-war party system is relatively intact.

In the wake of their expectation-smashing (maybe even 'mould-breaking') performance in Thursday's local elections, Ukip will be looming larger than ever in the minds of Conservative strategists. The wiser of them will turn to the history books to see what lessons can be taken from previous attempts to upset the parliamentary applecart. Yet history offers few lessons for the Tories, because Ukip present a new British political circumstance: a fractured right, from the right.

Historically the Tories have proved very, very good at cooperating with other parties to advance their agenda. At the turn of the century their alliance was built around the then-core electoral issue of Irish unionism. So dominant was this issue that the Tory-led governments of the period, especially those of Lord Salisbury, were termed 'Unionist' instead of Conservative, containing as they did the Liberal Unionists, the Irish Unionist Alliance, the Ulster Unionists, and the Scottish Unionists. In fact it is only by dint of a last-minute change of heart in 1912 that the party is not today called the National Unionist Party.

Following the war, they cooperated with and eventually co-opted the Liberal National and National Liberal parties, both centre-right breakaways from the collapsing Liberals. The National Liberals contested seats for the Conservatives until 1968, and Michael Heseltine fought his first election, in the Welsh seat of Gower, under the National Liberal banner in the 1959 general election.

Given that history, you might be tempted to give credence to the many voices on the Conservative right calling for some form of accommodation with Ukip, whether it is a merger, an electoral pact or something else. But the positioning is a critical difference. All the historical instances of the Tories working with and absorbing other parties have been with parties to the Tory left, including all three right-wing splits from the Liberals and smaller instances like the Scottish Progressives.

Ukip on the other hand, are a force of the nostalgic right. Many of the people urging Cameron to cooperate with Ukip are the same as those who rail against his cooperation with the Liberal Democrats, the Tories' coalition partners. What they see in a merger with Ukip is not the creation of a new iteration of Conservatism (as the ironically-labelled "purple plotters" saw in a Tory/Liberal Democrat merger) but the restoration of an old one.

This ideological lodestone, if not removed, stands to rob the Conservatives of one of their great historical secret weapons: freedom of manoeuvre. With their right flank in jeopardy, today's Tories cannot woo the right of the Liberal Democrats, nor the hard-pressed New Labour remnant, as once they might have. Instead, they are faced with a rival programme of populist fiscal fantasy. Like a right-wing equivalent of the pre-government Liberal Democrats, UKIP have built an unsustainable message: lots of new spending on things like prisons and the army; greatly reduced taxes; no advertised cuts to 'frontline services'; and no borrowing to bridge the gulf between their tax proposals and their spending ambitions. Like the Liberal Democrats they are exploiting the advantages of remoteness from government. Like the Liberal Democrats, that will bite them if ever they reach it.

On this reading, Ukip are in part an aspect of the new ideological inflexibility I identified as an important part of Margaret Thatcher's legacy to the British right. The result is that the Conservatives are caught on the horns of a dilemma: to appease Ukip is to woo a group most of whom were happily inside the Conservative tent as it threw away the 2001 and 2005 general elections on uncompromisingly right-wing platforms; yet to ignore it is to risk the further loss of voters, activists and even elected representatives on the right in circumstances that make it very difficult to pick up replacements on the left. On the other hand, it is very easy to see how chasing Ukip votes could shed centrist voters to the Liberal Democrats and Labour, which means that whilst Ukip are splitting the Tory vote it is impossible to simply add the two parties' poll ratings together to make the case for cooperation. Meanwhile, the oft-mooted panacea of a European referendum carries its own risks of engorging, rather than destroying, Ukip.

The other major reason that Cameron should be very wary of those calling for a Canadian-style 'Unite the Right' operation is that Ukip have not yet demonstrated the ability to win outside traditional Conservative heartlands. In Canada, even under first-past-the-post, the Progressive Conservatives and the Canadian Alliance were each able to win tens of seats in general elections and appealed largely to geographically discrete parts of the country.

By contrast, despite the fact that they've made some inroads amongst ex-Labour voters, Ukip's winning performance on Thursday was in rural England, the one part of the country the Tories aren't struggling in. Welsh Ukip couldn't muster any effort in Anglesey despite it being the only council in Wales going to the polls. There is as yet little sign of a Ukip breakthrough in the inner cities, Scotland, or Wales, whilst their one Northern Irish MLA is a defector.

If or when Ukip truly carry the centre-right standard deep into enemy territory, there might be grounds to consider some form of cooperation. But whilst they are simply contesting ground that Cameron's majority-less party already holds, wooing them amounts to little more than a core-vote strategy, the preserve of losers, and talk of a pact that involves handing Ukip Westminster seats is little more than a plot to overthrow Cameron's conservatism to restore a misremembered version of Margaret Thatcher's.

Henry Hill is author of the popular Dilettante conservative blog and was voted the UK's top Conservative and Right Wing student blogger in 2011.