The Telegraph reported that the National Security Council, which is chaired by May, had come to a decision on Tuesday that it would allow the Chinese company to contribute antennas and other infrastructure that are not considered to be part of the core.
The report said five ministers — Home Secretary Sajid Javid, Foreign Secretary Jeremy Hunt, Defence Secretary Gavin Williamson, International Trade Secretary Liam Fox and International Development Secretary Penny Mordaunt — had raised concerns about the company.
The news comes ahead of a planned meeting on 2 and 3 May between the US and European countries, where the former is set to reiterate its warnings about Huawei and Chinese technology in general being used in 5G networks.
Only Australia and New Zealand have fallen in line with Washington's dictates, but Wellington has indicated that the initial refusal for telco Spark to use Huawei gear is not the end of the matter. That stance was reiterated by Prime Minister Jacinda Ardern during a one-day China visit in April. Huawei sued the US on 7 March, seeking to be reinstated as a telco supplier in the country.
Earlier this month, the technical director of the UK National Cyber Security Centre slammed Huawei for its engineering practices, which he characterised as "very, very shoddy".
Appearing on the BBC's Panorama program, Dr Ian Levy said he had yet to be convinced that a remedial program, promised by Huawei to sort out issues that were identified last year, was going to be effective.
Huawei has set up a cyber lab in the UK, the Huawei Cyber Security Evaluation Centre. The HCSEC opened in November 2010 and aims to mitigate any perceived risks arising from the use of Huawei equipment in parts of the UK critical national infrastructure. The centre provides security evaluation for a range of products used in the UK telecommunications market.
In March, a report from HCSEC Oversight Board found "concerning issues" in the company's approach to software development, significantly increasing risk to operators and needing ongoing management and mitigation.
In February, Ciaran Martin, the head of the NCSC, said that any likely risk posed by Huawei was manageable.
"Because of our 15 years of dealings with the company and 10 years of a formally agreed mitigation strategy which involves detailed provision of information, we have a wealth of understanding of the company," he said.
Huawei Australia chairman John Lord welcomed the reported UK decision. "This is good news for UK consumers as they will have access to Huawei’s advanced and secure 5G networks," he said.
"Australia also needs all the leading suppliers competing to ensure we get the best technology at the best price."
In a statement, Huawei Global said: "Huawei welcomes reports that the UK Government is moving towards allowing Huawei to help build the UK’s 5G network. This green light means that UK businesses and consumers will have access to the fastest and most reliable networks thanks to Huawei’s cutting edge technology.
"While we await a formal government announcement, we are pleased that the UK is continuing to take an evidence-based approach to its work and we will continue work co-operatively with the government, and the industry."