I had something similar which I used through BHX a few times no problem but this year they were adamant you could only use the small bags they provided. No idea why, at the end of the day the liquids were still in the 100ml bottles and perfectly visible so what difference does the bag make?One of these:
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I saw one at Gatwick Airport a few days ago and thought they were a great idea.
However, my partner said she had one at Birmingham Airport a year ago and they wouldn't let it through until she put the cosmetics in one of those free bags they give out.