Events such as the brutal murder of Drummer Lee Rigby can often act as lightning rods in society, triggering a sharp shift in public attitudes and fuelling prejudice against minorities.

Many have suggested that the events in Woolwich have fuelled a wave of public hostility towards British Muslims and Islam more generally. But our findings, based on a YouGov survey undertaken within 24 hours of the attack, suggest that the picture is both more complex and more positive.

First, we find some evidence to suggest that, in the aftermath of these tragic events, Britons were more likely to think positively about community relations. There are some challenging results, such as the finding that the number of citizens who think that conflict between groups is "largely inevitable" has risen by seven points to 40%, or that agreement with the suggestion that there will be a serious clash between British Muslims and white Britons has also risen, by nine points to 59%. But these buck the broader trend.

Compared with last year, when we ran the same survey, people are now either just as likely, or more likely, to endorse a series of more positive statements: that Muslims are compatible with the national way of life; are good citizens; make important contributions to society; and share British culture and values.

In fact, while far-right groups were pointing to the murder as evidence that Islam poses a fundamental threat to modern Britain, the percentage of respondents who view Muslims as compatible jumped by almost 10 points to 33%. Clearly, the numbers remain low, and point to wider challenges facing government and our local communities. But in the aftermath of events that could well have triggered a more serious backlash, the direction of travel remains positive and suggests that there has not been a sharp increase in prejudice.

Second, we also find a very clear and sharp divide across generations. Whereas expectations of a future clash between Muslims and non-Muslims are especially pronounced among citizens aged 60 and above (at 70%), among 18- to 24-year-olds this figure tumbles to 48%.

Whereas only 21% of the older group view Muslims as compatible with British life, the figure among young Britons is almost twice as high, at 38%. Whereas almost half of the over-sixties view British Muslims as posing a serious threat to democracy, the equivalent figure among more recent generations is just 19%. Britain is in the midst of a silent and generational shift away from prejudice, although most of our political leaders remain focused on the short-term benefits to be gained by pitching to the older, and more prejudiced, voters.

Finally, while far-right groups appeared to profit from the tragedy, with the number of followers of the English Defence League on Facebook rising from 20,000 to more than 100,000, most people reject this toxic brand of politics. While the proportion of people who say they are aware of the EDL has risen since last year, an overwhelmingly majority – 84% – said they would "never consider" joining the group, which is up seven points since 2012. Similarly, only one out of every five respondents expressed positive views about the idea of counter-demonstrations to Islamist extremism. More than half rejected these actions.

Dr Matthew Goodwin is an associate professor at the University of Nottingham and advises the government on tackling race hatred