Eccles, I buy a packet of foil from Sainsbury's. It is ordinary extra strong. Nothing industrial about it.
No matter how I try to lift the seal carefully, it always rips the foil and spoils it. Maybe it's just me.......and Sibs
When the foil rips so that only half peels off you can easily waste 12 inches before you sort it out. Sometimes it takes a lot more than that to recover it
The sticky tape is there to prevent the aluminium foil from loosening on the roll between being packed and you buying it. Ever noticed how tight it is wound...if it loosened in transit, you'd lose a lot more than several inches because it's easily damaged.
midwives always used to grow one fingernail long, in case they needed to cut the frenulum under the tongue of a baby who looked as if it might be tongue-tied. Perhaps you could grow one to get under the sealing tape?