British Prime Minister Theresa May greenlit Huawei's involvement, with the National Security Council permitting Huawei "limited access to help build parts of the network such as antennas and other "non-core" infrastructure", The Telegraph said.
"It will report with its conclusions once ministerial decisions have been taken", Wright told parliament when asked about media reports.
But it seems the leaking of the decision by the National Security Council has not gone down well with government ministers, who according to the BBC, are calling for a "full and proper" investigation.
Hu Houkun, rotating chairman at Huawei, said last week that it had so far secured 40 commercial 5G network contracts, up from 30 announced in late January, and it has shipped more than 70,000 5G base stations, up from 40,000 announced in late February.
In contrast, GCHQ has repeatedly said Huawei needs to be closely monitored but has not called for a ban.
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.
Downing Street refused to say whether a leak inquiry was already under way but insisted the Prime Minister regarded the protection of information concerning national security as a "matter of the highest importance".
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Sir Richard Dearlove accused the Government of putting economic interests ahead of national security by allowing Huawei to supply technology for the 5G network.
Apparently, it has been confirmed from recent reports that Theresa May, U.K. Prime Minister, has chose to allow the 5G equipment manufacturer of China into the country's network.
The US has in effect banned Huawei from its 5G infrastructure.
Huawei's New Zealand deputy managing director, Andrew Bowater, was the most explicitly optimistic following the announcement on the eve of a trade mission to Beijing by United Kingdom chancellor for the exchequer, Philip Hammond, that Huawei could supply elements of the next generation of the internet, so-called "5G", as long as they were not core elements of the system.
Advisors from both the United States and the UK have voiced concerns about Huawei's involvement in any sort of infrastructure, citing fears that the company could be used for Chinese espionage.
Speaking on the Today programme, Mr Tugendhat said the proposals still raised concerns, as 5G involved an "internet system that can genuinely connect everything, and therefore the distinction between non-core and core is much harder to make".
5G requires a vastly different network architecture to 4G and other previous mobile networks, which is why the decision to limit Huawei to supplying some but not all aspects maybe become problematic to police.