The time travel thriller, which also stars Bruce Willis and Emily Blunt, pulls in more than £2.4 million to knock last week's number one movie ParaNorman off the top spot.
Resident Evil: Retribution, the fifth instalment in the video game horror franchise, bows at number three with £792,265. The total represents a significant dip from its predecessor Resident Evil: Afterlife's £1.69 million opening haul in 2010.
Will Ferrell and Zach Galifianakis comedy The Campaign debuts at number four, while Jennifer Lawrence's House at the End of the Street completes the top five.
Elsewhere, French comedy Untouchable climbs into the top ten as it expands its location count. The worldwide box office smash earns £317,979 from 153 sites across the UK in its second weekend on release.
The UK box office top ten in full:
1. (-) Looper - £2,427,994
2. (1) ParaNorman - £1,080,197
3. (-) Resident Evil: Retribution - £792,265
4. (-) The Campaign - £772,102
5. (3) House at the End of the Street - £545,961
6. (2) Killing Them Softly - £470,712
7. (5) Hope Springs - £423,051
8. (4) The Sweeney - £410,578
9. (7) Brave - £400,511
10. (17) Untouchable - £317,979
Watch Digital Spy's video interview with Joseph Gordon-Levitt below: