The four had been providing "free medical care and religious activities" in the Burutu area of Delta state, said Chief Theo Fakama, from the local Enukorowa community.
Fakama said locals were "saddened" by the kidnapping as the victims had "brought succour to residents of the community for the past three years".
The spokesman for Delta state police, Andrew Aniamaka, confirmed the kidnapping, which happened on October 13.
"The victims are of British nationality, two of whom are a couple, and have been rendering humanitarian services in the area for a while.
"But unfortunately, they didn't let the authorities know of their presence in the area all this while.
"There is a militant group that has been operating in the area and we believe they are the ones behind the abduction.
"Immediately the militants struck, they whisked the victims to the interior regions of the creek where we believe they are being held for the past five days."
It was unclear whether any contact had been made with the kidnappers or the motive for the seizure, he added.
Kidnapping for ransom has long been a risk in Nigeria's south, where high-profile individuals and their families are a frequent target for criminal gangs.
Victims are usually released after a few days once payment is made.
On October 14, the Vatican said an Italian priest was kidnapped by gunman just outside Benin City, which is the capital of Edo state and neighbours Delta state to the north.
Delta state commissioner of police Zanna Ibrahim told reporters in the state capital, Asaba, on Tuesday: "An anti-kidnapping team is already on the trail of the suspects."
He suggested the abduction could be linked to a recent military operation against violent crime, which has seen an increase in troops in southern Nigeria.
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