The survey asked 800 party members, the results of which were tested with a YouGov control panel.
Such polling is hypothetical for now as David Cameron is the clear leader of the Conservative party, but if he loses the election next May then a new leadership contest will take place. In fact, only this Sunday did a Telegraph article suggest that:
"Senior ministers are jockeying for position to succeed David Cameron as Conservative leader, as a new poll puts the Tories neck-and-neck with Labour.”
For now David Cameron is safe, but a loss to Ed Miliband next May will result in a hotly contested leadership battle. The poll puts Theresa May, the Home Secretary on a clear first place eleven points ahead of Boris Johnson.
Since the last poll, only last month, the gap between the front runners has widened significantly. The November poll put Theresa May ahead by just two points - 24% to Boris Johnson’s 22%.
In the event of a loss next year, it is likely that the new leader will be one of these three. May and Osbourne have the experience, and Johnson almost certainly has the charisma - and the ambitions - to lead the party.
If May does become leader, as these hypothetical polls suggest is possible, then she will be the second female Conservative leader. And perhaps the country’s second female Prime Minister.
Whilst May is not Margaret Thatcher, the truth is that the fact she is a Conservative woman will result in immediate comparisons with Thatcher being drawn by the media, and the electorate, if she becomes leader - or indeed just stands for the position.
On one hand, this could be beneficial for her and something she could take advantage of. Say what you like about Maggie, but she was a powerful figure and a strong leader. Whilst May is not Thatcher such comparisons are inevitable and could work well against the bumbling Boris Johnson, who has a very different sort of personality.
On the other hand, comparisons with Thatcher might not go down so well. Many regard her as a divisive figure, and whilst such comparisons might help May within her own party, appealing to other parts of the electorate - particularly those who would generally support Labour - will be a much harder challenge.
In the event of David Cameron losing the general election, who do you think is best placed to lead the Conservative party? Does Theresa May have what it takes?