Consumers have an average of three different insurance products split across three providers but most would still rather deal with just one firm, according to a new survey.
It noted that the rise of price comparison and aggregation services has changed the way people get insurance, including buying from multiple providers.
But the survey also found that customers want a more streamlined way to buy products through a single provider.
It highlighted that 86 per cent of the 2,500 people polled cited convenience, while 44 per cent said they would expect better prices for staying loyal, and 42 per cent pointed to added benefits or rewards for staying loyal to one provider.
When asked why they use multiple providers, 46 per cent said their provider did not offer different products, and 32 per cent said they did not feel there was any benefit to be had for staying loyal.
The online survey was conducted last September by consumer behaviour consultant Collinson Group.
It polled 2,500 members of at least one of the following loyalty programmes: airlines; hotels; or retail banking/credit cards in the United States, Britain, Singapore and the United Arab Emirates, and regardless of age and gender.
The Collinson Group said banks can capitalise by offering insurance products through loyalty initiatives, or value-added packaged accounts and credit cards.
Another Collinson Group global poll, this one of 6,125 affluent middle-class customers, also highlighted the opportunity for banks by showing there is a high perceived value for insurance products.
The online study was conducted early last year within the top 10 to 15 per cent of earners in Australia, Brazil, China, France, Hong Kong, India, Singapore, Britain, the US and the United Arab Emirates.
It found that 74 per cent of those polled in Singapore highly value health insurance, 69 per cent regard travel insurance in the same light and 60 per cent value assistance with lost cards.
It also noted that 45 per cent of customers rated identity theft protection as a highly valuable service, and that fears over data security influence what brands or products they use.
Mr Chris Rogers, director of market development at Collinson Group, said: "Due to the banks' substantial buying power, they can achieve economies of scale to deliver value across insurance products and pass this back to their customers.
"They can offer insurance at the low prices their customers expect due to a group risk approach, packaged as part of a bank account or credit card. This will provide differentiation, and builds on or leverages existing loyalty to the bank's core products - bank accounts or credit cards."
For instance, banks could offer travel insurance to a customer who has just booked a flight, or car insurance when one buys a car.
Mr Rogers added that this would be well received by customers, who have indicated in research that relevant offers are welcome, while consumers who like the idea of a "one-stop shop" also need to feel that the provider offers great value and quality products.