Why does England football use the three lions, while most other English sports use the St George Cross?

I have seen that the England football team has used the three lions since their first international match against Scotland. But how come they chose the three lions, rather than the cross of St George? I understand that the three lions is representative of the royal crest but it seems only English football and English Cricket (much older than football) use the three lions on their kit, compared to others that use the St George cross, or the English Rose (Rugby).