BT admitted last week that hundreds of people have encountered difficulties getting their flights, but insisted this was a very small proportion of those who had applied for their free economy flight to parts of the US or Europe.
The situation has been compared to the infamous Hoover offer of the early 1990s when many people struggled to get a free flight to America. Rise Travel, though, denies that the two episodes are similar.
A Rise Travel spokesman said on Wednesday that just one person had called a "dedicated number" set up by the company to handle complaints about the BT offer.
The spokesman wouldn't confirm BT's estimate that hundreds of people have been affected, saying "I don't have the figures to hand," but added that "severe Post Office problems" had hampered the processing of application forms.
Several ZDNet UK readers, though, have complained that they've not been able to get the flights they wanted, and have struggled to find out what is going on.
One reader says he ended up having to pay £400 for a flight to New York after being told that there were no more flights to America available all year, even though he submitted his application in plenty of time. He now intends to complain to BT and consumer protection associations once he returns from America.
One source close to Rise Travel has claimed that some customers have been waiting weeks to speak to the company, as the company's call centre staff were instructed just to pass details of complaints on to Rise.
The Rise Travel spokesman rejected this charge as "absolute nonsense". "We're not a fly-by-night company," he insisted.
Anyone seeking information from Rise Travel about a free flight promotion should contact the company on 01274 256058.