Claimed capacities for batteries are bunk – my battery charger tracks actual charge taken and many of the higher capacity AA’s i’ve had (reputable brands) are no better than batteries with a lower claimed capacity.
My experience is that there’s a big variation in quality of Li-Ion/Polymer batteries and most of the ‘non-genuine’ batteries i’ve bought (laptops, NIMH for makita drills, iPod, Nokia/Sony phones) have been significantly worse than the genuine article. They’ve not delivered the charge promised and had a much shorter life than the original items they replaced.
Add to this that there are a lot of fake batteries doing the rounds means trying to save money by buying the real thing cheap is risky.
Personally, I’d take the phone to an Apple store and pay them £50 to do it.