The first Battle Round edition of the talent show was viewed 764,000 times in one 24-hour period, as the singers went head-to-head for a spot on the live shows.
Demand for The Voice UK outstripped the previous single-day iPlayer record of 623,000 requests set by Sherlock episode 'A Scandal in Belgravia' in early January, reports Radio Times.
Linear TV ratings for The Voice UK on April 21 were down by around 800,000 viewers on the previous week's show, but it appears that many people used iPlayer to catch up on the show.
This follows a blog post last week by acting Sky Atlantic controller Naomi Gibney, in which she claimed that linear TV ratings are "far less important than once was the case".
Gibney made the comments while defending the low ratings for the fifth season of Mad Men on the pay-TV channel, saying that the programme actually attracted a larger audience when factoring in Sky+ recordings and video on-demand.
The BBC regularly reports its audience figures using a Live+7 system, which collates the overall consumption of programmes across live, catch-up TV and PVRs.
For example, an episode of The Apprentice aired on May 25 last year commanded a total audience of 10.15m viewers over its seven-day period using Live+7 data, considerably more than the 7.46m on just overnight figures.
Photo gallery - The Voice Top 20: