The ad, created by agency AMV BBDO, depicts the remarkable true story of real events that took place on Christmas day 1914, when troops on both sides of the conflict downed their weapons, emerged form their trenches and exchanged seasonal songs and gifts. The two armies also played friendly games of football to mark the festive occasion, an image also featured in the ad.
The Advertising Standards Authority assessed the complaints received, but has decided there are not grounds for investigation and is closing the case.
In a statement the UK ad watchdog adds: "While we recognize that some have found the use of the First World War for advertising purposes to be distasteful, the ad is not likely to break the rules surrounding harm or offense. We also considered that the ad is obviously distinguishable from editorial content and is therefore not likely to mislead."
Alongside the TV campaign, Sainsbury's has partnered with the Royal British Legion to sell the vintage-looking chocolate bar that appears in the ad in stores for £1, with 50p of each purchase going to the charity.
Sainsbury's told Marketing Week earlier this month that it was selling 5,000 of the chocolate bars every hour.
The ad has been viewed more than 12 million times on YouTube, although many of the comments below the video are critical of the choice of storyline. One user, Beckie02, writes: "I wish this wasn't an advert... :/. The motivation behind it's [SIC] creation sullies it. It feels a bit tasteless/wrong...As a video on it's own, it's good."
However, there are also swathes of users praising the ad in the YouTube comments.
You can watch it yourself here: