Ed Vaizey told a gathering of MPs, “I’m not going to guarantee to you that every single premise is going to get 10 Mpbs but it should be potentially possible.”

Last year, the Government promised that everyone should have the legal right to request a 10 Mbps connection by the end of this Parliament, no matter where they live. Mr Vaizey said then that this could come into force as early as 2017.

But when MPs on the culture, media and sport committee asked if this could be truly universal, he suggested limiting the amount of public funding available on hard-to-reach properties.

Mr Vaizey also admitted to “significant delays” in the DCMS’ Broadband Delivery UK (BDUK ) unit, which hands out subsidies to make delivering superfast broadband in rural areas economically viable.

He said BDUK is currently “on track” with its target to cover 95pc of Britain’s geography with superfast broadband by 2017, which it defines as achieving minimum speeds of 10 Mpbs.

But he blamed delays in rolling out internet on local authorities, saying that councils took too long to negotiate contracts. Negotiations were “extremely time-consuming and significantly delayed the project,” he said. “I should’ve intervened much earlier.”

This latest hearing comes one day after Sharon White, Ofcom’s chief executive, faced the same group of MPs, who asked about the regulator’s plans to reform BT Openreach.

Ofcom has proposed sweeping changes to further distance Openreach from BT, for example, by giving the division control over its own finances, but Ms White said discussions with BT are still in their “early stages” and may not reach a voluntary agreement.

Ms White did not set a deadline on negotiations but said that a timescale of when to expect changes would be available later in the summer.

Gavin Patterson, BT’s chief executive, also faced a grilling from the cross-party committee last month during which he admitted that Openreach misses 1,000 repair appointments a week.