Ofcom has called on Openreach to move away from copper-based broadband networks and invest more heavily in fibre.
According to Sharon White, Chief Executive of the watchdog, Openreach must replace its "Victorian-era" copper infrastructure and switch to a modern full-fibre alternative.
Otherwise, she believes the organisation risks losing "swathes of customers to full-fibre rivals", ISPreview.co.uk reports.
"Incumbents face a choice in my view - fibre up or risk fading away," Ms White commented.
"History is strewn with once-successful companies that failed to anticipate and act on shifts in customer demands and to innovate. Think Kodak, Polaroid, Palm and Blockbuster.
"The UK cannot afford for BT to be added to that list."
Ms White went on to note that good progress on boosting full-fibre availability across the UK is being made.
Indeed, she pointed out that in the next few years, the number of homes and businesses able to benefit from the technology is set to rise from one million to six million.
However, Ms White said this remains "some way short of the ambition that full-fibre is available nationwide".
"So we must build on the early momentum," she stated.
Earlier this year, Openreach pledged to make fibre-to-the-premises (FTTP) broadband, which offers speeds of up to 1Gbps, available to three million premises by 2020.
The organisation believes this will set it "on the right trajectory" to achieve its goal of building a ten million FTTP footprint by the mid-2020s.
However, Ofcom recently said it needs to be "more ambitious" and credited smaller broadband providers with kickstarting the shift towards greater full-fibre broadband access.
Speaking to the Financial Times, Ms White said smaller companies have taken a lead on rolling out full-fibre infrastructure and established themselves as "disruptors" in the broadband market.
This, she said, has helped to "shake up the complacency of the incumbent", as the likes of Openreach are now stepping up their focus on the technology.