Wright said that such leaks endangered the ability of the committee, made up of senior ministers and which hears regularly from intelligence agency bosses, to get unequivocal and frank security advice from experts.
However, Ms James said she was not "biased against" Huawei and that "banishing" one supplier would not solve security concerns.
The decision is also a rebuke to the USA government, which has pushed for its allies to block Huawei and other China-based tech giants from 5G networks around the globe.
It also reported that various ministers had raised concerns about the plan.
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In the past the United Arab Emirates and Egypt have supported Haftar with air strikes during campaigns to take eastern Libya. World Health Organization said on Wednesday it would send medical staff to treat the wounded, whose number has reached 913.
GCHQ's Fleming said the United Kingdom needed to gain the public's trust in order for it to become a powerful cyber actor, noting the country "must have the legal, ethical and regulatory regimes to foster public trust - without which we just don't have a licence to operate in cyber space".
"We're at a fork in the road".
The U.S.is keen that Five Eyes members do not involve Huawei in 5G development, as it could afford the Chinese Communist Party regime a back door to spy on their activities. But for many, the partial ban does not go far enough.
The information was briefed to the Daily Telegraph from Tuesday's meeting of the national security council, which is top secret and classified.
Huawei Australia chair John Lord added that consumers in the United Kingdom will benefit from the Chinese networking giant's "advanced and secure 5G networks".
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"We've set out that objective independent technical assessment of what's needed and I'm confident ministers will reach a decision that will provide for the type of safer 5G networks that we need".
The news comes despite the Home Secretary, as well as the Defence and Foreign Secretary have all expressed concerns over the green light the government has given the Chinese firm.
Downing Street has not confirmed that an inquiry will be held, but Culture Secretary Jeremy Wright told MPs: "We can not exclude the possibility of a criminal investigation here and everyone will want to take seriously that suggestion".
The move follows a recent report from the oversight board of the Huawei Cyber Security Evaluation Centre (HCSEC), which warned that "further significant technical issues" had been identified in Huawei's engineering processes, leading to "new risks in the United Kingdom telecommunications networks" (full summary).
It appears that the government may have changed its mind about allowing a Chinese firm to play a part in a massive technology infrastructure project.
Google to let Android users in EU choose browsers
Android of course is the widely used mobile operating system in the world, by some margin, well ahead of Apple's iOS for example. Users who choose a search app will also be asked if they want to change the default search engine in the phone's Chrome browser.
Last year, the United States, Australia, Japan, and New Zealand all banned Huawei from participating in government contracts, citing security reasons, while several other countries said they were also anxious about Huawei's activities.