More than a third of radio listening (33.9%) is now via digital platforms, such as DAB radio, digital TV, and online.
But sales of DAB radios, which account for the lion's share of digital listening, have been flat at 1.9m for the past four years, according to media regulator Ofcom's digital radio report, published on Wednesday.
Among radio listeners who do not have a DAB radio at home, 58% of them were either unlikely or certain not to but a set in the next 12 months.
The statistic – set against 14% of people who said they were likely or certain to buy one – is an indicator of the scale ahead as the government looks to achieve a 50% target for digital radio listening before a road map to switchover from analogue can become a reality.
The Ofcom report said four in 10 new cars now have DAB radio fitted as standard, but that two thirds of all radios sold last year had no DAB tuner.
Overall sales of radios slumped in 2012 by 1m to 5.6m in the year to the end of June, 2013.
The drop can be attributed to a decline in analogue radio set sales, which fell to 3.7m, but was still nearly double the number of DAB sets sold.
The proportion of people claiming to have a DAB set at home has gone up 4% to 45.7%, said the report, which is published annually by Ofcom.
This year's report comes ahead of a keenly anticipated government announcement, due in November, confirming its policy on digital radio and switchover.
The findings of the 2013 report reveal that while the top digital stations have increased their listenership, as reported in the latest Rajar figures, sales of DAB sets have failed to accelerate over the year.
According to Ofcom, ownership of digital sets varies across the UK, ranging from 54.4% in Surrey to 18.1% in the Border region.
Broken down demographically, it is those in the AB social group which are most likely to listen to digital radio at least monthly, while in terms of age, 16- and 24-year-olds are the most likely to listen.
The report also found that four in 10 (38.3%) of new cars are fitted with DAB as standard, an increase of nearly a third from 2012.
The report highlighted recent Rajar figures which revealed that BBC 6 Music has usurped BBC Radio 4 Extra as the UK's most popular digital radio station.
BBC 6 Music is now the most widely listened to digital station, boasting an average weekly reach of 1.74 million listeners, up from 1.6 million in 2012, trumping BBC Radio 4 Extra, which reached 1.66 million listeners, up from 1.6 million.