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I've replaced the battery and screen (for someone else) in an old iPhone before (although I know it changes based on the model) and on my Garmin Edge 705 GPS. I'm fine with intricate work like this. I have a set of suitable tools/spreaders/etc. Phone is in otherwise good condition.
It's a £43 saving (as I just ordered a battery for under £6) for doing it myself compared to getting Apple to do it. With a replacement battery it'll be like new anyway, and I don't mind if that only lasts another year or so as I'll be looking to replace the entire handset by then anyway.
Have you taken a phone apart before?
It's very fiddly and you need to buy a quality set of screwdrivers.
Also if the phone is old and not in good general condition you can get stuck quickly.
Not to say don't give it a crack, but just know it's not going to cost a tenner and if others are getting new phones for £50, it seems hard to justify the £20-30 saving unless you really need that money.