My brother has lived in Spain for more than twenty years. My parents are buried there, and spent the last fifteen years of their lives there. I'm certain that they did not, and do not, carry their passports around with them. In many European countries — including France — the rule you've specified exists on paper, and it is followed more in the breach than in the observance.
By the way, I agree that anyone from the UK attending the match should not take any risks, and should have their passport on them. I am not inciting people not to.