Update
Package was delivered yesterday, the same item as in that video.
I watched a YouTube video of fitting a new battery and dived in. The little sucker in the kit to remove the screen was crap, so I used a bigger one that was here and it worked fine. The glue that holds the battery in place just pulls outs, but the second strip split, which meant I had to pull the battery out with my fingers. I was worried it would break as it was stuck, but it came out eventually, all twisted. No probs, though. The little screws are very small but the screwdrivers had magnetic tips which helped a great deal. Put in the new battery and it all worked perfectly. Took about 30 mins, 10 without the screen hassle.
I let it run down to 10% then fully charged it this morning. There's still 84% charge remaining after 6 hours, being out in the cold and being used on and off.
Also in the kit was a charging cable, screen protector (a thick one) and all the tools. For £8.90 it's a result. Apple can kiss my old battery !