April's figure has nearly double the 750,000 users recorded during the online player's first full month of operation in January.
The total number of requests for downloads and streams of BBC programmes in April was 21m, rising from 17.2m in March and 11.2m in January.
According to BBC data, there are slightly more users in the 35-54-year-old category than the 16-34 category. The former group contained 43% of users and the latter 37%, while the over-55s contained 21%.
The list of the top 20 most requested programmes was dominated by 'Doctor Who' and 'The Apprentice' from BBC One, but six BBC Three programmes also featured.
Among the BBC Three programmes was an episode of comedy series 'Gavin and Stacey', which received around 250,000 requests for download or streaming in the week it won the Bafta Audience Award for Programme of the Year.