Later this month, Ukip will descend on the northern Labour-held town of Doncaster to hold its annual conference. The party has good cause to celebrate. Since its last conference in 2013, at which Nigel Farage was overshadowed by Godfrey Bloom, Ukip has made a serious advance in British politics. The party won the European parliament elections, has since revamped its front team and now, after the defection of Douglas Carswell in Clacton, looks set to win its first seat in parliament. But how has support for Ukip been evolving during all this?

To answer this question we can draw on the prestigious British Election Study, which has just released the results of its latest survey, undertaken after the European elections. This means we can compare the findings to surveys earlier in the year to explore how support for Ukip has changed, if at all. There are three important messages.

The first is that over the period of the European parliament elections, Ukip’s appeal widened along the political spectrum (as some of us have been arguing). Former Conservative voters continue to provide the bulk of support to Farage; of those who voted Conservative in 2010, 20% say that they are planning to vote Ukip in 2015 (up from 17% in February).

But since the beginning of the year, Ukip has also been winning more support from disaffected Liberal Democrats and Labour voters. By June, almost a quarter (22%) of Ukip’s support came from voters who previously chose one of these two parties. Of the two, the shift from Labour supporters to Ukip has been the most significant, increasing from 5% to 11% at the time of the European elections.

Meanwhile, support among Lib Dem voters for Ukip has increased from 11% to 13%, providing further evidence that Ukip is possibly beginning to attract the protest element of the Lib Dem base. Clearly, many of these voters might only have switched to Ukip for the European elections. The challenge facing Farage is to convert them into long-term supporters, while the task facing the main parties is to win them back.

The second message is that the anti-Ukip campaign appears to have had no significant effect on how the British public feels about Ukip or Farage. Before the European elections, 25% of respondents said they “liked” Ukip and 23% liked Farage. When these voters were surveyed again after the European elections, 28% liked Ukip (+3%) and 27% liked Farage (+4%). Despite repeated attempts to portray the party in a negative light, Ukip and its leader actually became more likable in the eyes of the public. In fact, Farage managed to outperform both David Cameron (whose likability increased by 0.2%) and Ed Miliband (whose likability declined by 2% during the same period).

But it is not all good news for Ukip. The final message from the data is that Ukip continues to face challenges ahead of 2015. On one level, support for it has remained stable since the European elections. Contrary to the predictions of commentators such as Dan Hodges (who promptly declared after the famous LBC interview that “Farage is finished”), the number of voters who say they plan to vote Ukip in 2015 has risen, from 12% in the pre-European election period to 16% post-election.

But there is a slight decline in the percentage of Ukip voters who plan to stay loyal at the 2015 election; this is down five points to 52%. While this level of support is sufficient for Ukip to affect the outcome in 2015, Farage will need to be thinking of ways to ensure this decline does not continue.

Interestingly, it is women who appear especially nervous about supporting Ukip. While there is some evidence that Ukip was successful in closing the gender gap by appealing to more women at the European elections, it is women who are now the most likely to abandon the party. Before the European polls, 62% of female Ukip supporters planned to stay loyal but that is down to 53%, a drop of nine points (men dropped two points to 51%). Whether Ukip’s new female spokespersons, such as Suzanne Evans and Louise Bours, will stem this decline remains to be seen. But what is clear is that Ukip’s support is far from static, and as the party approaches the 2015 election it may yet see further change.

• Caitlin Milazzo’s byline was mistakenly left off this article. It has now been added.