The British flag has no lions at all. I assume you mean the Royal Arms of England, which does have three lions.
It's not clear that they "represent" anything at all... William the Conqueror used two lions passant guardant (walking, looking out at the viewer) as his blazon. It was the symbol of the Duchy of Normandy, of which William was Duke.
The third may be the Lion of Aquitaine, the symbol of the Duchy of Aquitaine. Eleanor, wife of Henry II, was Duchess of Aquitaine in her own right, and her son Richard appears to have combined the two lions of Normandy with the single lion of Aquitaine in the Great Seal of England, and the three lions were used by several later kings as their personal arms.
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The lions on the badge are dark blue, and they are surrounded with red and white English roses.
The lions on the badge are dark blue, and they are surrounded with red and white English roses.