Communications regulator Ofcom has opened a consultation into whether BT's Openreach service should be split off into a separate company
Most internet service providers offer services through a fixed-line network controlled and maintained by BT.
But Ofcom said it had concerns BT Openreach's performance on behalf of those providers had often been poor.
BT chief Gavin Patterson told the BBC that he thought splitting the Openreach service off would be a "mistake".
Following Ofcom's last strategic review 10 years ago, BT was obliged to create Openreach through which it provided access to its telephone and broadband network to "competing providers on equal terms".
Essentially, those providers pay a wholesale price to BT for use of the network and then charge telecoms customers for services.
Analysis: Kamal Ahmed, BBC business editor:
Sky and BT don't like each other very much, particularly since the latter took a healthy portion of Sky's lunch by piling into sports television and winning the rights to broadcast Premier League matches.
There are dark mutterings that BT uses the vast profits from Openreach to fund its incursion into television, a claim the company hotly denies.
BT insists that Openreach's service has improved, with 2,500 engineers added in the last year and 700 more coming this year. It says it reaches or exceeds all of the 60 service targets set it by Ofcom.
And that it is only because of BT's large and healthy balance sheet that so much investment has been made in upgrading the network to super-fast broadband.
What won't be superfast is the Ofcom process. This is the latest stage in a far wider review of the UK's digital market which will take months to conclude and years to implement.
Read more from Kamal's blog here:
BT is responsible for connecting almost all households to the network regardless of their service provider, as well as improvements to and maintenance of the network.
However, Ofcom said the network had evolved in recent years, with the growth of fibre optic cable services - particularly in towns and cities - offering television, telephone and superfast broadband internet services.
And problems remain, with rural areas regularly complaining about poor internet service provision and BT's chief rival Sky claiming it can take up to 10 days for Openreach to connect new customers.
BT chief executive Gavin Patterson told BBC Radio 4's Today programme he believed it would be a "mistake for the country as a whole" for Openreach to be split away from his company.
He said 88% of the country now received superfast broadband and that BT had put forward proposals to deliver the next stage in delivery of services - known as ultra-fast broadband.
Key to the delivery of that, he said, was the scale that a company the size of BT could offer.
He rejected claims that BT enjoyed a monopoly on internet service provision, saying the "BT brands have less than a third of the market so I don't think there is a problem at all."
And he pointed out BT's biggest rival Virgin Media served more than three million customers in the UK.
But Mai Fyfield, Sky's chief strategy officer, welcomed the consultation adding that "consumers and businesses have been suffering because the existing structure does not deliver the innovation, competition and quality of service that they need".
She added: "We believe Ofcom should now move quickly to ask the Competition and Markets Authority (CMA) to undertake a full competition inquiry."
The consultation follows the introduction of new rules, which Ofcom announced at the start this year, designed to ensure that BT could not price rivals such as Sky and TalkTalk out of the market.
BT is still awaiting the outcome of a Competition and Markets Authority (CMA) investigation into its takeover of mobile phone operator EE.
If the takeover goes ahead it would create the largest mobile phone network in country and give BT the ability to offer "quad play" services - fixed line telephone and broadband internet, television and mobile phone services - in competition with Virgin Media and Sky.
Sky and BT have also entered into a bitter rivalry over pay-TV services, particularly for lucrative sports, in recent years.
Last year, BT outbid Sky for exclusive rights to show Champions League football matches on its BT Sports channels from August. Earlier this year Sky was forced into a very strong bid to maintain its hold over the rights to the majority of Premier League football matches.