The Conservative party has held onto London's City Hall for the best part of a decade. It is a remarkable achievement in a city which was previously considered a Labour stronghold.

However, all the signs are that the party is rapidly giving up any remaining hopes of holding onto it once Boris Johnson stands down next year.

Attempts to find a suitable candidate to succeed Johnson have so far come to nothing, with all the leading figures either unavailable or unwilling to stand.

Top of the list was Sebastian Coe. Both Johnson and the Tory leadership spent several years trying to convince Coe to go for the job. However, all of these attempts appear to have come to nothing after he announced his intention to campaign for the presidency of the International Association of Athletics Federations instead.

The result of that contest will not be announced until August 2015, by which time a campaign to become mayor seems unlikely, even if he were interested.

Candidates count themselves out

Johnson's second choice is Conservative backbencher and established troublemaker Zac Goldsmith. Goldsmith has the charisma, cross-party appeal and spending power to campaign for the job. He would be a canny choice and both Johnson and those around him have repeatedly urged him to go for the job.

However, he has made enemies among the current leadership and friends of Goldsmith have made it clear that he would not consider standing until 2020. Two other candidates lined up for the job have also declared themselves out of the running. London Assembly Members and current Johnson appointees James Cleverly and Kit Malthouse are both set to leave London to stand to become Conservative MPs this May. A third possible candidate, businessman and TfL appointee Michael Liebreich has not yet ruled himself out but is believed to have gone cold on the idea of standing for mayor this time.

This leaves the Tories scrabbling around to find a possible third choice. So far three candidates have declared an interest in the job. None of them are household names.

First up is Conservative London Assembly member Andrew Boff. Boff is a deeply independent politician who sometimes takes unpredictable positions on London politics. For instance, one of Boff's long-held beliefs is that the London mayoralty is a "dictatorship" which should be abolished. 'Vote for me - I don't think this job should exist' would be an interesting argument for a Tory candidate to make, but it seems unlikely he will get a chance to make it.

Second to declare their interest is millionaire businessman and gay rights campaigner Ivan Massow. Massow was previously involved in Steve Norris's failed bid to become mayor. However Norris is at pains to distance himself from him now and he appears to have little obvious support in the party. Like Boff, Massow also has a line in eye-catching policies, one of which is to turn City Hall into a homeless shelter. While London could certainly do with some more homeless shelters, I somehow doubt this particular building will ever be one of them.

Third to declare their candidacy is the mayor's current policing deputy Stephen Greenhalgh. Greenhalgh is probably the best known of all the remaining candidates, having previously been the leader of Hamersmith and Fulham council.

However, he is a controversial and divisive figure. Two years ago he was forced to apologise after I revealed that a female member of staff had complained to colleagues about him inappropriately touching her in a City Hall lift. No formal complaint was ever made, but the issue continues to be raised in interviews. His prickly style has also acquired him a number of enemies at city Hall, chiefly among his own party. Conservative London Assembly members have fallen out with him both in private and public, while even Boris Johnson himself was involved in disputes with him this week over police funding and tube fares.

The prospect of him emerging as the Tory candidate has already motivated some of his rivals to consider running as a "Stop Greenhalgh" candidate.

However, the prospect of Tessa Jowell emerging as Labour's candidate appears to have already put off potential Tory candidates from standing. Opinion polls have shown Jowell has a clear record of cross-party support and she is widely admired by Tory politicians, including Johnson himself. Many Tories also share the belief popular among Labour supporters that Boris was a one-off and that City Hall will inevitably return to Labour after he leaves. The prospect of Jowell being the candidate has only deepened that assumption. If she is selected later this year then the Tories could end up only standing a token candidate.

This would be a huge error on their part. There have so far been four mayoral elections and Labour have won just one of these. The London mayoralty is not the property of any one party. It is a presidential rather than a party system. If the Tories can find a decent candidate then there is no reason why they can't win a historic third term.

But even if they can't manage that feat, Londoners deserve a proper contest in 2016. The Conservative party should ensure they get one.