Popular and affordable
The number includes households in Northern Ireland for the first time, which accounts for 400,000 of the total.
Broadband uptake has been fuelled by a host of attractively priced offers from companies such as Carphone Warehouse, BT and BSkyB.
"The market share of broadband connections has been increasing ever since 2001, reflecting its growing popularity, affordability and widespread availability," the ONS said in a report, based on information from internet service providers.
The South East of England has the largest internet penetration of any region with 66% of households now online, while Scotland has the lowest with 48%.