The Advertising Standards Authority has widened its inquiry into the advertising of the Apple iPad.
The BBC understands the regulator is not satisfied that Apple has complied with an agreement to amend claims about the latest iPad's 4G capabilities.
The UK does not yet have widespread 4G coverage, and the iPad will be incompatible with it when it does.
The regulator said it had received dozens of complaints in relation to the issue. Apple has declined to comment.
The regulator had resolved some of the complaints after discussions with Apple about changes to its advertising, but said it is now looking into further concerns raised by consumers.
A letter to one complainant seen by the BBC says that Apple "have advised us that no further reference to the 4G capabilities of the iPad will be made on their UK website".
The letter goes on to say that this will resolve the complaint, and the Advertising Standards Authority (ASA) will consequently be closing the file.
The ASA told the BBC that when it approached Apple the company said it had removed references to 4G from the webpage subject to the complaint, and had edited a video that contained references to 4G.
But Apple's UK site still offers consumers the chance to buy a "wi-fi + 4G" version of the iPad.
A footnote explains that "4G LTE" is supported only on certain networks in the United States and Canada.
The ASA said it had since been contacted by several complainants who had identified other "potentially problematic claims" about the iPad and 4G on the website.
"If it appears that the problem claims we asked Apple to remove are still appearing," the regulator said, "we will investigate these new complaints."
Apple said it would not comment on its discussions with the regulator, but a source at the company insisted that no undertaking was given to remove all references to 4G from its site.
4G mobile phone networks, which promise much faster web surfing, have yet to arrive in the UK.
But even when they do, the frequencies to be employed for the new networks in Britain - and the rest of Europe - are different from those used in the US and Canada.
That means that the "4G" iPad, in its current configuration, can never connect to 4G networks in Europe.
Apple is also in dispute with Australian regulators over the advertising of the iPad there.
The country's Competition and Consumer Commission accused the firm of misleading consumers by telling them that the product could connect to a 4G network in Australia when that was not the case.
Apple offered to refund any iPad buyers who felt that they had been misled.