And one in five of those allergic reactions (19 per cent) resulted in a hospital visit.
But the survey by the Food Standard Agency (FSA) and Allergy UK showed there have been improvements for those with allergies since new labelling rules came in.
The EU Food Information for Consumers (FIC) legislation, which came into force in December 2014, means that catering firms have to make information on 14 allergens available to customers.
The rules cover the most common allergens, such as peanuts and gluten, as well as lesser known triggers for allergic reactions such as mustard and celery.
Around two million people in the UK suffer from allergies, including one in 50 adults (two per cent) and eight per cent of children.
The survey, conducted to mark Allergy Awareness Week, found that five out of six people (83 per cent) reported noticing an increase in measures designed to make life easier for people with allergies - including menus marking out allergens, and staff actively checking food information with the kitchen.
More than half (58 per cent) said that their overall experience of eating out has improved; just six per cent said it has got worse. As a result, a similar proportion (52 per cent) say they now feel more confident eating out than they did before the legislation was introduced.
However, people with allergies still report a number of problems when dining out.
More than two-thirds (69 per cent) have experienced staff not understanding the severity of an allergy, and how easily a mistake can cause a reaction.
A similar number (68 per cent) have seen staff with a lack of knowledge of what's on the menu or in the food - including staff confusing eggs with dairy, or assuming that the customer was asking for gluten-free rather than avoiding lupin - a grain commonly used in place of wheat.
More than half of people with allergies (56 per cent) said they've been made to feel like an inconvenience due to their allergy.
In total, around a third of those with a food allergy have suffered a reaction in the last year when eating out of the home. The vast majority of these took place in a restaurant or cafe, with nine per cent being a result of takeaway food. In most cases the reaction was self-treated, but 19 per cent resulted in a hospital visit.
Dr Chun-Han Chan, the FSA's food allergy expert, said: "Allergies can be fatal, and this is why it is vital food businesses give their customers information they can trust.
"It's been more than a year since the introduction of this legislation and we're pleased to see real progress in how food businesses provide information on allergens to their customers.
"In general, the situation is improving for the two million food allergic consumers in the UK, and greater numbers have the confidence to eat out.
"However, our survey has found that this isn't true for everyone, and that many establishments aren't yet providing the information that their customers need.
"The number of people suffering from food allergies and intolerances has increased in the last decade, so it's clear that it is not something businesses can ignore."
Dr Chan said if anyone encounters a food business not providing information on the 14 allergens, they should report it to the local authority which will investigate. The survey showed that those affected are currently more likely to report it to staff in the first instance (69 per cent) or complain on social media after the event (23 per cent).