The Advertising Standards Authority (ASA) has received dozens of complaints from users about "potentially problematic claims" regarding 4G in the iPad on Apple's UK website.
Last month, Apple was rebuked by a watchdog in Australia as the new iPad is being heralded as supporting 4G connectivity, but this is actually only available in the US and Canada.
UK consumers are currently unable to access 4G LTE, a new spectrum technology enabling superfast mobile internet on smartphones and tablets.
There is a proposal to make 4G available in Britain later this year, but the new iPad's 4G connectivity will still not work if the service launches as it will not be configured for European 4G frequencies.
The ASA therefore contacted Apple to request that all mentions of 4G were removed from UK marketing.
Apple said that it had complied with the request, removing several 4G references from its website and editing a video that contained references to the connectivity, but the BBC reports that the ASA is unsatisfied with the company's response.
The watchdog had resolved an initial flurry of complaints, but has now said that it could re-open the investigation after fresh objections from consumers.
Apple's UK site still offers consumers the opportunity to purchase a "WiFi + 4G" version of the new iPad, although a note explains that "4G LTE" is only supported on certain mobile networks in the US and Canada.
But the ASA has also been contacted by several complainants expressing concern about other "potentially problematic claims" about 4G in the iPad on Apple's UK site.
"If it appears that the problem claims we asked Apple to remove are still appearing, we will investigate these new complaints," said the ASA.
Apple declined to give official comment, but a source within the company told the BBC that Apple had never agreed to remove all references to 4G from the site.
However, the US technology giant opted to offer refunds to any iPad buyers in Australia who felt misled by the 4G claims, after the country's Competition and Consumer Commission threatened to take the firm to court.