The bi annual research shows the number of consumers listening to radio in this way has increased steadily over the past two-and-half years.
The Midas 5 research reveals 17.4 million consumers listened to radio via the internet in November, up 3% from 16.9 million in May and up 8% from 16.1 million in October 2008.
Of the 13.9 million people who use "listen again" services, 74% said it had no impact on the amount of live radio they listened to and half said they were now listening to radio programs they did not previously listen to.
The number of users of personalised online radio services such as Spotify and Last.fm has increased to 4.5 million, up 15.4% from 3.9 million in May and 55.2% from 2.9 million in October 2008.
The research showed 8.1 million people have downloaded a podcast. Of these podcast listeners, 78% said their podcast listening had no impact on their live radio listening and 33% said they now listened to radio programs they did not listen to previously.
The research involved 977 respondents from the main Rajar survey who claimed to have listened to the radio via the internet or downloaded podcasts, as well as respondents from the previous two Midas surveys.