BT has offered to make high-speed broadband available to the one million-plus rural homes left behind in the internet revolution, potentially accelerating the process by which every household will have access to fast connections.

BT’s subsidiary Openreach, which controls the UK’s broadband network, has told ministers it will spend £600m to ensure 1.4 million rural homes have access to a minimum speed of 10Mb by 2020, meeting a Conservative pledge.

Under the current Tory plan the final 5% of homes and businesses that do not have access to decent speeds – mostly in locations where it is uneconomical for providers to extend their services, such as parts of rural Wales, Cornwall, Yorkshire and Scotland – would only be connected in a slow trickle from 2020 onwards.

For now the government intends to continue to press forward with its regulatory approach – under which households will have to go through a slow process of requesting access – while also consulting on BT’s proposal, which would make 10Mb available to the final 5% in one go.

A spokesman at the Department for Digital, Culture, Media and Sport said that if any potential deal was done with BT it would not abandon a manifesto pledge that every household has a legal right to fast internet. The government said it will not sign any potential contract with BT unless that legal obligation is transferred to the company.

“We warmly welcome BT’s offer and now will look at whether this or a regulatory approach works better for homes and businesses,” said the culture secretary Karen Bradley. “Whichever of the two approaches we go with in the end, the driving force behind our decision-making will be making sure we get the best deal for consumers.”

On Friday, a group of more than 50 MPs, led by former Tory party chairman Grant Shapps, published a report claiming that as many as 6.7 million households do not get the broadband speeds they pay for. Shapps’s report said that Ofcom, the regulator, should make providers such as BT, Sky and TalkTalk pay compensation if they fail to deliver promised speeds.

BT’s proposal does not include any public funding. Previously taxpayers footed a £1.7bn bill to put fibre optics between local exchanges and roadside cabinets across a quarter of the country where BT said it was not commercially viable.

Instead, BT is proposing to recover its costs, which it estimates at £450m to £600m, through higher charges to rivals such as Sky and TalkTalk, as well as BT’s own broadband unit, to use Openreach’s national network.

Rivals argue that this is a stealth charge that effectively means UK broadband users will fund the rural internet rollout as their bills go up.

In March, Ofcom published proposals to force BT to cut almost £100m in charges to rivals using Openreach, which could result in millions of broadband customers seeing their bills slashed.

The regulator is consulting on the proposals, which BT has not supported, and rivals claim that BT’s offer to the government will aim to reverse those planned cuts in charges. The government has asked Ofcom to look at BT’s plans on how to recover its rural broadband rollout costs as part of its existing review.