Can I put my T-mobile payg simcard in an O2 contract iphone 4s?

My mum is giving me her old iphone 4s, she is currently on an O2 Contract and I have a T-mobile PayG simcard.
I understand that because of the different networks it will be locked, or something like that, but because they're different types of simcards, is there any way it would possibly work?
Like sending it away to get it unlocked. Or would I have to ether get a T-mobile contract or just an O2 PayG simcard?

Sorry if this doesn't make sense…

Added (1). Just saying nope isn't gonna help. Explaining a little might.
And I've heard you can get your simcard cut anyway?

Nope

Not all phones take exactly the same type of SIM card - so you do not even have a guarantee that it will fit into the phone.

You probably would have to get it unlocked first at a provider like www.iphoneunlockedcheap.com who does O2 and other carriers.

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