Ofcom plans to enforce price controls on one of Openreach's most popular broadband lines to help drive investment into superfast broadband.
The telecoms watchdog will cut the wholesale price BT's infrastructure arm can charge rivals such as Talk Talk and Sky for lines with a download speed of 40 megabytes per second and an upload speed of 10 megabytes per second.
The move will see prices charged for the line falling from the current level of £88.80 per year to £52.77 per year in 2020/2021.
Ofcom said it expected companies to pass down the costs savings to customers in the form of lower bills.
Jonathan Oxley, Ofcom's competition group director, said: "Our plans are designed to encourage long-term investment in future ultrafast, full-fibre networks, while promoting competition and protecting consumers from high prices.
"People need reliable phone and broadband services more than ever. We're making sure the market is delivering the best possible services for homes and business across the UK."
Openreach will maintain full control over the prices for lines with an even faster speed in the hope that it will spur telecoms firms towards installing their own superfast lines to rival BT.
BT is instructed by Ofcom to allow rival broadband firms to use the Openreach network to sell internet services to customers.
The price controls come as part of a package of new rules demanding Openreach fixes faults and rolls out broadband lines at a quicker pace.
As part of the measures, Openreach will be expected to improve the level of fault repairs completed within one to two working days from 80% to 93%.
It also wants 97% of repairs to be completed within six to seven working days, while lifting the number of lines installed on the date agreed by Openreach and the telecoms firm to 95% from 90%.
BT was hit with a record £42 million fine by Ofcom on Monday and is facing compensation costs to rivals of £300 million over delayed high-speed cable installations.
Ofcom found Openreach had committed a "serious breach" of its rules for reducing payments owed to other providers such as Vodafone.
The telecoms giant was supposed to pay compensation after failing to deliver high-speed lines to the rival companies in adequate time.
The huge sum is the largest fine issued against a telecoms provider by Ofcom and almost 10 times larger than the previous record, a £4.6 million penalty against Vodafone last year.
Openreach questioned whether the price controls would lead to fresh investment in superfast broadband.
A spokesman for Openreach said: "Ofcom have proposed a number of ways to address fibre pricing and service so we will be reviewing these in detail, but on first viewing they don't appear to incentivise more investment in 'full fibre' networks.
"The UK needs a regulatory framework that encourages investment and rewards risk. Building digital infrastructure is very expensive with long payback periods and we won't recover our more than £3 billion investment in fibre until after this charge control period.
"We want to invest in more 'full fibre' infrastructure, and we'll be consulting with our CP customers to develop new business models and support to achieve that.
"We support the ambition of higher service targets and we want to work closely with the rest of the industry to make sure these are the right measures and that they're achievable."
Talk Talk chief executive Dido Harding said the price cuts were welcome, but consumers will be left frustrated that they have to wait a year before they can benefit from lower bills.
She said: "Ofcom's decision to only regulate some products also risks entrenching a speed divide, with customers having to make a false choice between fair prices or higher speeds.
"Ensuring consumers enjoy low prices on all superfast products is the best way to maximise take-up and encourage investment in the pure fibre infrastructure of the future."