YouGov surveyed nearly 2,063 adults. The survey also suggested that 18 per cent of the remaining UK analogue TV subscribers would switch to Freeview HD.
Freeview will launch an HD service in the next six weeks. It is planning to initially offer three HD channels - BBC, ITV1, and Channel 4. Channel Five may be added at the end of the year.
Nearly 10 million UK homes already rely on Freeview to receive digital TV.
Freeview will market with the strapline "Buy now, watch today, free forever".
Freeview managing director Ilse Howling has reportedly said that the company would also consider launching a 3D service, depending on the viewer response to Sky's 3D channel, which is due for launch in April.