Britton is in line to make his 400th appearance for the Swans against Reading, having initially joined the club on loan from West Ham in December 2002.
"It's an important game for us," Laudrup told reporters on Thursday.
"We are playing at home, against a direct rival, and we want to win.
"These are the games that we have to get points from. We want to get back to the way we were playing in the first three games because that is very important.
"If we can do that then we can win on Saturday.
"He (Britton) is an institution at the football club and there are not many players that play for so long at one club, particularly in the modern era, so it is great.
"400 games says a lot. Let's hope we can give him a day to remember by winning the game."