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It will; GiffGaff use the O2 network.
EDITED BECAUSE I'M AN IDIOT - I read "phone" as "iPhone" for some reason and so assumed that the original poster was talking about an iPhone, but they don't actually say "iPhone" anywhere in the message.
The following is therefore only useful information if it is actually an iPhone - if it isn't, please ignore!!!
However, it's still worthwhile using the opportunity to get the phone unlocked. If he's currently on pay monthly unlocking is free, and if he's on PAYG it's £15 (not £20). Once the unlock has taken place he can then move to _any_ network at all at a future date without having to even ask the question you've asked or mess around with any other unlocking method. It's the only way to get a proper factory unlock.
I'd say it's probably worth the outlay to get that factory unlock - especially if they are on pay monthly right now, as the outlay is zero.
Edited to add: forgot to give the URL, d'oh. http://shop.o2.co.uk/update/unlockmyiphone.html
tesco mobile uses the o2 network aswell so you should be good to go
Tesco phones still need to be unlocked as they are "double locked" even though they are carried by the O2 network, like 3 (which is the same) and won't work with a giffgaff sim