The expansion of high-speed 4G data networks, which allow video clips from YouTube or Vine and TV on-demand services such as BBC iPlayer and Netflix to be watched more easily on the go, is driving the change, a report found.
A third (33%) of internet access in 2015 was through the multi-purpose handsets, up from 23% in 2014, especially among younger age groups, according to Ofcom's 2015 Communications Market Report.
The phones overtook laptop computers in popularity, with the larger devices falling from 40% of online connections in 2014 to 30% in 2015. Two-thirds of adults now have a smartphone, up from 39% in 2012, and the amount of time we spend using them to go online has risen to one hour and 54 minutes per day.
Jane Rumble, director of market intelligence at Ofcom, said the change in internet access was a "landmark moment".
She said: "You can see these devices are becoming more and more an important vital hub of information and communication throughout the day, with smartphone owners spending almost two hours (on them) each day, almost double the amount of time that those people are spending on their laptop or desktop.
"The key driver of this change is coming from age groups, particularly the young age groups. Those aged 16 to 24 are much more likely, as well as 25 to 34s, to say their smartphone is the most important device to get online, whereas for the older age groups, they are much more likely to be sticking with their laptop.
"This is a landmark shift.
"Interestingly, you can also see amongst the 55 to 64s there has been growth as well, so half the older age group now own a smartphone too."
More than a third of all adults (34%) use their smartphone within five minutes of waking up, a figure that rises to almost half (49%) of those aged 18-24, the report's research found.
Subscriptions to 4G, which was first introduced in the UK in 2012, rose eightfold from 2.7 million in the last quarter of 2013 to 23.6 million in the last quarter of 2014, as it became more widespread.
The 4G technology allows video content and streaming services to be watched on the handsets, which older, slower connections could not handle without irritating buffering.
Almost two-thirds (62%) of 4G phone owners told Ofcom they "couldn't live without it", compared to 52% of all smartphone users.
"It really is becoming an important and vital device throughout the day. The increase in 4G subscriptions has been very stark in the last year," Ms Rumble added.
It was not just smartphones which reported increased use for online access, as tablets rose to 19% in 2015, up from 15% in 2014 and 8% in 2013.
Both laptops and desktop computers declined, with desktops now accounting for just 14% of internet use.
The report also showed society's increasing digital connectivity. The total amount of time people spent online rose from 9.9 hours per week in 2005 to 20.5 hours per week in 2014.
However, traditional television remains the entertainment king. The average adult watched three hours and 40 minutes of television per day in 2014, 11 minutes less than in 2013. Last year was the second year in a row the watching time had declined.
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