The presenters were seen sipping gin and tonics in a Toyota pick-up truck during their attempt to become the first people to drive a car to the Magnetic North Pole as part of the show's Polar Special last year.
At one point, May said to Clarkson: "Slow down while I cut the lemon".
They raced against Richard Hammond, who was making the same journey in a sled pulled by dogs.
'Top Gear''s executive producer said that they were beyond the jurisdiction of drink-driving laws in international waters and that the pair were neither drunk nor out of control at any point during the making of the programme.
Following a complaint from a viewer about the "blatant use of alcohol", the BBC Trust ruled that the scene "was not editorially justified in the context of a family show pre-watershed".
The trust's report from its editorial standards committee, said: "The committee took into account that the situation -- a trip to the Magnetic North Pole -- was far removed from the ordinary experience of viewers and that the drink was included on one occasion for entertainment purposes as a comic device to play up the relaxed travel of those in a car compared to the presenter who was travelling by sled.
"However, the committee was nonetheless concerned that, given some children might regard the presenters as role models, the scenes could be seen to glamorise the misuse of alcohol."
The trust ruled that repeats of the show should not be shown pre-watershed unless this scene was edited out.
The same viewer also complained about a scene showing a frostbitten penis but the trust said that "there was a clear editorial purpose for the use of the image in that it was used for a medical rather than a sexual purpose".
The latest complaint about Clarkson follows his acquittal for a speeding offence. He had been accused of failing to name the driver on a speeding ticket sent to him by car company Alfa Romeo.
The company said he had been loaned a car caught by a speed camera travelling at 82mph in a 50mph zone on the A40 in Ruislip, west London, last October.
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