Icomera, the company supplying the Wi-Fi service to GNER, reported on Monday that use of the service was growing at 77 percent week on week.
"Obviously it is early days for the service but these figures are very encouraging," said GNER director Shaun Mills in a statement.
This rapid growth is partly caused by an increase in the number of trains offering the service, with six having been upgraded so far. But the evidence from customer feedback is that train Wi-Fi is a hit.
"We are seeing an increase week-on-week of the actual time spend online by users. There's also evidence that people are upgrading to first class to use the service for free," said Peter Kingsland, wireless consultant at BWCS, a telecommunications consultancy firm which has worked with Icomera on its Wi-Fi service.
Kingsland explained that a significant number of mobile workers are on the cusp of travelling in first class, and are tempted to upgrade to avoid paying £4.96 per hour for Wi-Fi in standard class. Dodging the hassle of paying online by credit card and renewing the subscription every 30 mins is also a factor, he said.
Just over 70 percent of people using the GNER Wi-Fi service have been checking and sending email, while 42 percent have been accessing corporate networks and 30 percent have been checking GNER's online travel information. Instant messaging has also been a popular application.
Icomera's service uses a satellite downlink to the train, and mobile phone networks for the uplink back to the Internet from the train. There are coverage blackspots in tunnels, but despite this Icomera says that 67 of people surveyed said they would definitely use the service again, and 88 percent said they would recommend it to friends.
Train Wi-Fi is a fast-growing sector, with companies such as Broadreach and 21Net also targeting the UK's train operators.
Magnus McEwan-King, chief executive of Broadreach, told ZDNet UK last month that his company had raised enough cash to Wi-Fi-enable up to 700 trains and has signed deals with five UK train operators including Virgin.
Kingsland, though, says that GNER and Icomera are well ahead of their rivals.
"The competition in the market may be talking a good game, but there's little evidence of Wi-Fi trains on the tracks," said Kingsland.