Conservative critics of Boris Johnson’s Huawei decision will push for a commitment from the government that the Chinese firm must be forced out of Britain’s telecoms infrastructure within three years.

Johnson defied the US and rebels in his party on Tuesday by deciding to allow Huawei to build part of the UK’s 5G network as long as it is restricted to “non-core” parts of infrastructure and has no more than 35% of market share.

A group of anti-Huawei Tories want an assurance that the government will work towards reducing the Chinese company’s influence in UK infrastructure to zero, ultimately stripping it out of the 4G network as well.

Their argument is that any provider deemed high-risk by the intelligence services should be phased out of the supply chain, although Britain’s spy agencies say that any security risk from Huawei can be managed.

Unhappy MPs held a series of meetings in Westminster on Tuesday night after Johnson’s announcement to discuss tactics, although they are keen to operate behind the scenes to push for a concession without embarrassing No 10.

If Downing Street does not offer assurances, several senior Tories believe they have a chance of getting the 45 rebels needed for a successful backbench revolt on legislation relating to regulation of Huawei.

They are looking at forcing a Commons vote on legislation expected next month to set out Ofcom’s powers to monitor the 5G network, potentially laying an amendment to toughen the proposal that Huawei would be limited to a 35% market share per mobile phone operator.

Among the public critics of the Huawei decision are the former party leader Iain Duncan Smith, the former Brexit secretary David Davis, and the former defence secretary Penny Mordaunt, as well as Tom Tugandhat, the chair of the foreign affairs committee, and Damian Green, Theresa May’s former deputy.

Green told BBC Radio 4’s Today programme: “One of the things that frankly surprised me was the breadth of opposition to the current stance of the government on the Conservative backbenches.”

The culture secretary, Nicky Morgan, toured the airwaves on Wednesday defending the government’s decision, saying the cabinet was “clear-eyed” about the risks of Huawei as a vendor with links to the Chinese state.

She argued that Britain’s security services had already been dealing with Huawei in the 4G network for years and therefore it did “not present the security challenge that others are worried about”.

Q&A What is Huawei and why is its role in 5G so controversial? Show Fast-growing Huawei is arguably China’s first global multinational. The Shenzhen-based company makes mobile phones, base stations and the intelligent routers that facilitate communications around the world. But its success increasingly concerns the US, which argues Huawei is ultimately beholden to the Chinese Communist party and has the capability to engage in covert surveillance where its equipment is used. Huawei is by some distance the world’s largest supplier of telecoms equipment with an estimated 28% market share in 2019. It was also the second largest phone maker in 2019, after Samsung and ahead of Apple. But Australia banned Huawei from 5G in 2018, with its spy agencies declaring they were worried the company could shut down power networks and other parts of its infrastructure in a diplomatic crisis. Trump banned US companies from working with Huawei last year and has strenuously lobbied others to follow suit, venting “apoplectic fury” in a phone call to Boris Johnson after the UK agreed to allow the Chinese company into 5G. The company had successfully targeted the UK early on. It has supplied BT since 2003 and gradually expanded to the point where it agreed to create a special unit in Banbury, known as the Cell, where the spy agency GCHQ could review and monitor its software code. Vodafone is another key customer. Britain’s intelligence agencies said in January that any Huawei risk could be managed as long as the company was not allowed to have a monopoly. As a result, Boris Johnson concluded Huawei’s market share should be capped at 35% for forthcoming high-speed 5G networks. In July 2020 the UK position changed, and it was announced that Huawei is to be stripped out of Britain’s 5G phone networks by 2027. Oliver Dowden, the UK culture secretary, also announced that no new Huawei 5G kit can be bought after 31 December 2020 – but said that older 2G, 3G and 4G kit can remain until it is no longer needed. Dan Sabbagh Defence and security editor Photograph: Mark Schiefelbein/AP

However, that has not reassured many Tory backbenchers, who are concerned that the US and Australia have banned Huawei over fears China could use the company’s role in the network for spying.

Ben Wallace, the defence secretary, vociferously protested against the move in the national security council meeting on Tuesday, although he eventually signed up to it as part of collective responsibility.

The re-election of Tugendhat, one of the government’s fiercest critics over Huawei, to the chairmanship of the powerful foreign affairs committee, is also likely to increase the pressure on ministers.

Tugendhat warned earlier in the week that allowing the Chinese firm a role in building the 5G network would be akin to “letting the fox into the hen house, when really we should be guarding the wire”.

He was one of several senior, independent-minded Tories elected to key committee posts after elections among MPs on Wednesday. Johnson’s leadership rival Jeremy Hunt is the new chair of the health select committee, and former defence minister Tobias Ellwood will chair the defence committee.

Any rebellion would require around 45 Tories to defy Johnson over the decision when legislation relating to Ofcom’s oversight of Huawei comes to the House of Commons.

One senior Tory told the Guardian he feared there was a risk that China could use information gleaned from 5G to identify blackmail targets. “A lot of [other Conservatives MPs] have said to me it is right to criticise this. At the moment the government has certainly not won the argument, put it that way,” he said.

The government announced its unanimous decision on Tuesday after a meeting of the national security council. Huawei’s share of the new market will be capped at 35% for each of Britain’s four mobile phone operators, and it will be banned from core parts of the telecoms network and from sensitive sites, including nuclear and military facilities.

Huawei was formally deemed a “high-risk vendor” because its Chinese ownership meant Beijing could in theory force it to carry out surveillance of British citizens in the future.

In spite of reservations on the Tory benches, Johnson appears to have averted a full-blown public confrontation with the US government over Huawei. The Trump administration had given a series of strongly worded warnings about the security risks in the run-up to the decision, but was prepared to soften its stance after a phone call between Johnson and Donald Trump on Tuesday afternoon.

Sources said that while the US remained disappointed with the decision, the security and economic relationship between the two countries was too important to jeopardise in a row over mobile phone technology.

UK and US sources said the two countries would try to work together to further reduce the use of Huawei in Britain. Downing Street hopes it has been able to persuade the notoriously unpredictable US president not to escalate the issue.

But leading Republicans have criticised the decision. Newt Gingrich, the former speaker of the House of Representatives, said it amounted to a “major defeat” for the US. Tom Cotton, a Republican senator, described the decision as like allowing the KGB to build the UK’s telephone network during the cold war.