A video released early on Sunday purported to show the aid worker being beheaded by Islamic State (IS) militants.
Mr Haines, 44, was seized in Syria in 2013 and was being held by IS militants, who had already killed two US journalists.
Tearfund has been working with refugees from Syria since violence broke out there, but only returned to Iraq this summer.
It is looking to support the tens of thousands who have fled their homes.
Many were faced with the prospect of converting to Islam, paying a tax or being killed.
Spokesperson Katie Harrison, who recently visited Iraq, told Premier's News Hour that the charity takes security very seriously but that it is not planning to change course.
She said: "There is a job to do; we believe God has called us to do it.
"We believe we should go where the need is greatest and serve as many people as we can, as well as we can, and we will continue to do that."
She was speaking as world leaders agreed to help Iraq defeat IS militants using "any means necessary". Ministers from 30 countries met in Paris.
The extremists are still threatening to kill Alan Henning from Manchester, who was kidnapped after travelling to Syria as part of an aid convoy.
Hear Katie Harrison's full interview on Premier's News Hour: