Martinez is a former Swans manager.
Britton said: "It'd be strange if we went up there and got a result that dented their survival chances.
"We've good links with Wigan. Obviously Roberto was well thought of as a player and manager here. He's responsible for a lot of what happened to this club reaching the Premier League.
"He changed the way we trained and got us passing.
"Other managers have played big parts as well, but Roberto started a lot of it and deserves a lot of credit. The assistant boss, physio, coaches, Jordi Gomez - there are a lot of people there with links to Swansea.
"But we must try to get a win so we'll concentrate on doing that."