The Welsh side start the new Premier League season with a home game against the champions on Saturday, when much of the focus will be on David Moyes after he got the nod to succeed Alex Ferguson at United.
Moyes faces one of the toughest jobs in world football in trying to continue the level of success enjoyed at Old Trafford under Ferguson.
That has prompted some to speculate that United could struggle initially, but midfielder Britton is in no doubt that Saturday's opponents will feel they have a point to prove at the Liberty Stadium.
"People ask is it a good time to play Manchester United, but you have to remember they are the champions and won the league by 11 points last year," the 30-year-old insisted.
"Yes, they have changed their manager but they have not changed their players that much.
"We couldn't have asked for a much tougher game.
"It's all eyes on Manchester United to see how they start under a new manager. It's a new era.
"You saw the job David Moyes did at Everton over the last 10 years. He didn't have the biggest budget, but they always finished very highly under him."
Swansea held United to a 1-1 draw at home last season and are in good form, having won all of their seven friendlies in pre-season and reached the UEFA Europa League play-offs with a 4-0 aggregate win over Malmo.
