Insurance firms are facing increasing competitive pressure on all fronts due to the emergence of a number of insurance technology (insurtech) start-ups, according to a report.

With the integration of technologies like artificial intelligence, blockchain and drones entering the insurance mix, the sector is being forced to rethink its model.

The World Insurance Report, published Wednesday by consulting giant Capgemini and non-profit industry body Efma, found that nearly one third (31.4%) of customers relied on insurtech solutions - either exclusively or in combination with an established insurance company.

"Customers are seeking more digital touch points for convenience, as customers experience in their daily lives that degree of personalization," Keith Webb, vice president at Capgemini and co-author of the report, told CNBC via phone call Tuesday.

"And the insurance industry can't actually lag behind, although I think that it still is lagging behind other sectors. But certainly it's waking up to the fact that working in partnership with more insurtech firms - working in partnership with technology firms generally - through their innovation labs now which are fairly common, is definitely enabling more rapid, and more innovative engagement models with customers, that take them into that personalization stage that really customers are beginning to expect."

There are several accelerator programs such as the U.K.'s Startupbootcamp and Germany's Allianz X (part of the Allianz group) which mentor insurtech businesses and help them scale up.

Insurtech, an offshoot of the financial technology (fintech) sector, is a rapidly evolving movement aimed at simplifying and improving the efficiency of insurance.

But the report also found that more traditional insurance channels still found favor with many consumers. Out of the 8,000 consumers surveyed by Capgemini and Efma, 46 percent said mainstream insurance firms performed better than insurtech vendors at security and fraud protection, while 44 percent said they performed better than insurtechs at brand awareness.