Steve
As you say the peaky blinders on television are a fictional account of a well known at the time Birmingham gang, they were not the only notorious gang of the time the Sloggers were another among others.
As has been stated the practice of sewing razor blades into the peak of their caps is in doubt, but it is a well spread rumour because I was aware of it in my early teens. I suppose that coming from the slum areas where these gangs originated might have been the reason why these rumours still persisted in the area.
It must have been a dangerous practice if true and you would have had to have been careful when putting your cap on or taking it off. I was in my early teens at the end of the Teddy Boy era and has a mate who carried a cut throat razor one of the top pockets of his drape jacket. It was more for show than use as a weapon and he was always getting it out and waving it about. I remember one day when he reached into his pocket to impress some girls and stupidly when putting it away previously he had put it in upside down and it had opened slightly in his pocket. When he pulled out his hand his finger had been sliced right down to the bone. He spent the rest of the evening in A&E having his finger sewn back up.