The state-run Anatolia news agency said the Pakistani suspects had been detained last week in a raid on their homes in Istanbul's central Mecidiyekoy district.
Police then expanded the operation based on intelligence the suspects provided and detained the British suspect, identified as Hasan H, at a bus stop in the conservative Fatih district, it added.
All have now been remanded in custody by a court.
Anatolia said that Hasan H was believed to be linked to Aine Lesley Davis, a close associate of the notorious British IS militant known as "Jihadi John" who Washington believes was likely killed in a recent drone strike in Syria.
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There has been no further information on Davis' case since his detention.
Long criticised for not doing enough to stem the flow of jihadist fighters across its volatile border with Syria, Turkey has stepped up fight after a number of deadly attacks on Turkish soil blamed on IS, making almost daily arrests of would-be jihadists.
Earlier December the government said that over 2,700 jihadist suspects from 89 countries had been detained in Turkey and deported.