Vodafone has said it is experiencing a 30% rise in internet traffic across its UK fixed-line and mobile networks.
More people are working from home as a result of the coronavirus pandemic, putting more demand on all networks.
TalkTalk, another internet provider, said that its daytime network traffic had risen 20% since Monday.
One EU official has suggested that online TV services should stream content in lower resolution to protect broadband infrastructure.
On Wednesday evening, European Union commissioner Thierry Breton called on content providers to switch to standard definition feeds to prevent networks from being overloaded.
But the internet providers have played down suggestions that they cannot cope.
Use of remote-access technologies, webmail and video-conferencing apps are taking their toll.
Vodafone says spikes in usage are “largely the same” as before in terms of the total amount of data being uploaded and downloaded.
But the “busy hours”, which normally run from 18:00 to 20:00, now extend all the way back to lunchtime.
“We have enough headroom to meet growing demand and to keep the UK connected,” a spokesman told BBC News.
“Our network team is keeping a constant watch on the situation.”
Other network operators have noted streamed television and games downloads still make use of considerably more bandwidth.
One of the most popular corporate video chat apps, Microsoft Teams, typically requires 0.5-1Mbps, while streaming a TV programme in 4K and high dynamic range (HDR) can require a constant rate of 20-44Mbps.
The forthcoming launch of Disney+ in the UK, which will offer 4K-resolution content, and the BBC’s plans to provide classes for children online because of schools being suspended, could therefore put the networks under more strain.
However, TalkTalk rejected the idea that its systems were at any imminent risk.
“We continually optimise our network for both our consumer and business customers and are well prepared to ensure they receive reliable connectivity,” it said.
That does not mean that every service will necessarily run smoothly.
Blizzard – the company behind multiplayer games including World of Warcraft and Overwatch – reported its service had suffered as a result of a cyber-attack.
And the company had previously warned users “may experience increased waiting times” as a result of a decision to allow staff to work from home because of the Covid-19 outbreak.
Epic said its video game Fortnite had also experienced multiple issues lasting about three hours on Tuesday.