The victory puts the O'Moore County on the verge of promotion to Division Three.
Laois had to "dig deep" to secure a fifth consecutive league win, according to their manager Justin McNulty.
London kept Laois within range throughout the first half with a solid defensive display.
Facing into a stiff wind for the second period, and leading by just three, the O'Moore County had plenty to do.
A quickfire four points, including an Evan O'Carroll goal, sent Laois towards another victory in Division Four.
The final score was 2-12 to 0-9 points.
McNulty says his side have to improve in possession.
He joined Midlands 103's Pat O'Sullivan to review the Laois performance:
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