The regulator has released its annual snapshot of online and media habits in the UK, which this year spans all three lockdowns.
It found 20% of children did not always have access to a device for online learning while schools were closed.
Ofcom said in total 6% of the homes had no internet access at all, at the time the study was carried out last month.
There were also 1% of adults aged over 18 who had internet access but chose not to use it.
Those without access were most likely to be either people aged over 65, or households with low incomes or financial vulnerability.
Among children, tablets were the most popular device for five to 15-year-olds in 2020, although 91% of 12 to 15-year-olds had their own smartphones. It was also found that 48% of three to four-year-old pre-schoolers had their own tablets.
Just over half of 12 to 15-year-olds said they had had a negative experience online in the past year, with the most common being someone they didn't know trying to befriend them.
Six out of 10 five to 15-year-olds said they made their own videos online and nearly half said they watched content on TikTok.
"We have seen a big rise in the use of TikTok during last year particularly among girls," said Yih-Choung Teh, strategy and research group director at Ofcom.
"The perception among adults is that it's focused on younger people but adults have increasingly taken up TikTok as well."
According to Ofcom, 21% of its adult social media users had TikTok profiles, although Facebook was the most popular overall with 83% of the adults in the study having a presence on the platform.
Gaming also became increasingly popular during lockdown, with 62% of adults and seven out of 10 five to 15-year-olds playing online games.
The campaign group Which? said it was very concerned about those who were getting left behind.
"It is vital that more is done to address this digital divide and ensure all consumers are able to access broadband connectivity, particularly as new networks roll out across the UK," said Rocio Concha, director of policy and advocacy.
Former Prime Minister Gordon Brown, whose Alliance for Full Employment has released its own report on the digital divide, called for a national digital plan from the government and Ofcom.
"We have a generation that has lost out for more than a year on the education that they need, and will lose out when it comes to workforce qualifications, job prospects, and then income," he told the BBC.
"So we've got to heal this digital divide. And I think the government's got to act pretty quickly."
Good news - the year of the pandemic has seen a big fall in the number of homes without any internet connection as the need for services only available online has become more acute.
Bad news - those who are still living without the internet find themselves even more disadvantaged than before. And that applies particularly to children. While hardly any now live in homes without any internet connection, a substantial minority had either poor and expensive connections via mobile phones or devices that were inappropriate for online schooling.
This digital divide became a hot political issue during lockdown and there will be continued pressure on the government to make sure children have the digital tools they need.
But this report also shows that children are providing a forecast of where our media habits are heading.
It's a future dominated by video-on-demand and video sharing services such as YouTube and TikTok, with plenty of them creating content rather than being just passive consumers. However, broadcast TV was less and less of a habit - even in lockdown, it seems, fewer families were gathering on the sofa for a big TV moment.
But while there are concerns about the dangers in this era of ultra connectivity - half of 12 to 15-year-olds had had a negative online experience such as being contacted by a stranger - there are also signs that this generation is pretty clued up about how the online world works.
They were not far behind adults in recognising which results in Google searches were ads, and probably more savvy in realising that when an Instagram influencer plugs a product they are being paid for that.