The proportion of super-fast connections - which offer headline speeds of 30Mbit/s or more - has risen from 5% in November 2011 to 25% in November last year.
The average superfast connection speed has also continued to rise, reaching 47Mbit/s by November 2013 - up 47%, or 15.1Mbit/s, since May 2010.
Ofcom's 10th report measuring consumers' actual broadband connect-ion speeds reveals that the average UK residential speed is 17.8Mbit/s, almost five times faster than five years ago.
But while the growth in average speeds shows investment in broadband technology is delivering benefits for most consumers, the UK picture is uneven, Ofcom said.
The average speed in rural areas rose from 9.9Mbit/s to 11.3Mbit/s between May and November 2013.
The sizes of the rural samples from which these averages were taken are not large enough for the change to be deemed statistically significant. As such, the figures should be treated as indicative only, Ofcom said.
One key reason for the slower speeds in rural areas is the limited availability of superfast broadband services.
Ofcom chief executive Ed Richards said: "The growth in superfast broadband and the rise in average speeds is testament to the investment in the sector.
"But the benefits are not shared evenly across the UK. There is more work needed to deliver wider availability of broadband and superfast broadband, particularly in rural communities but also in some locations within cities."
The Government is committed to improving speeds in rural areas and has pledged funding to ensure superfast broadband is more widely available across the UK.
Communications Minister Ed Vaizey said: "We are investing £790 million to ensure that 95% of the UK will have access to superfast speeds by 2017."