The film, which stars Tom Hanks and is based on the Dan Brown novel, took £2.97m on its opening weekend.
But The Girl on the Train held on to the top spot for a second week, after taking £3.41m.
Screenings of the West End production of Miss Saigon took £2.03m - the biggest-ever debut for an event cinema release, according to Screen Daily.
The stage production was simulcast to celebrate the show's 25th anniversary performance.
Animated children's film Storks, which features the voices of Jennifer Aniston and Kelsey Grammer, debuted at number three.
Bridget Jones's Baby took a further £1.88m in its fifth week, keeping it in the top five.
The film has now taken £42.24m to date - surpassing the £42m taken by Bridget Jones's Diary, the first film in the series, which was released in 2001.
Further down the chart, American Honey debuted at number 10 with £175,000, while Finding Dory jumped back up to number nine after taking £187,000 in its 12th week of release.
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Inferno has failed to topple The Girl on the Train from the top of the UK box office.