The Board of Deputies says it is being hampered in the collection of Jewish birth statistics because not all mohelim (circumcisers) are providing figures for brits performed each year.
The number of births is based on the annual circumcisions performed by mohelim registered with the respective Orthodox and Progressive societies.
But Daniel Vulkan, the Board's research and information officer, who helps to compile its demographic reports, said there were a number of mohelim who either had not re-registered with the Orthodox-run Initiation Society, or had never been members.
"We don't know how many there are," he said. "But a few who have left continue to operate independently. I think it is a problem because some of those who haven't re-registered carry out fairly large numbers of circumcisions, based on figures in the past."
From anecdotal evidence, he said, "the reason they aren't renewing their membership is because the premiums are going up".
Membership of the society is £275 a year, which includes insurance.
But Alex Minn, secretary of the Initiation Society, argued that the numbers of those who had not re-registered "could be counted on one hand". He also believed that they were more likely to be those who performed only one or two circumcisions a year. But Mr Minn conceded that mohelim were not always "very prompt" in re-registering. "Sometimes we have to send as many as three reminders," he said.
The Board - which reported 3,205 Jewish births in the UK for 2005 - is now trying to gather data for births for 2007. Over the past couple of years, there has been growing debate, in particular, over exactly what proportion of British Jewish babies are to strictly Orthodox parents.
Mr Vulkan explained: "Each year we try to collect the number of circumcisions carried out around the country. We assume that the ratio of male to female births in the Jewish community is broadly the same as the general population, so from the circumcisions we calculate the number of births overall."
Chanoch Kesselman, executive co-ordinator of the Union of Orthodox Hebrew Congregations, the umbrella body for London's strictly Orthodox communities, said that most approved mohelim belonged to the Initiation Society.
"Of the 36 certified by us, there may be just three or four who are not members of the society - and they are ones who probably don't do general communal circumcisions.
"There are some who have learned to be mohelim and do it just for their family because they want to keep the precept that a father should circumcise his son," he said.