I don't even think it has to be running like crap. From what I understand, if you book yourself into an Apple store, tell them it's running slow and you'd like a new battery. They'l probably suggest you erase it and start again but if you insist on a new battery, they'll fit one.
Assuming the £25 offer isn't extended beyond 2018, I reckon the last few months of the year are going to be really busy with people doing this.