Britton played for Martinez when he was in charge of the Swans.
"No-one should be surprised at what's doing there, certainly not people who've worked with him," he said. "The lads who he brought here still think very highly of him. People who know him, know what he is like as a person and as a manager know the impact he can make.
"He's had a terrific start. It wasn't an easy task taking over from someone who had been in a job for 10 or 11 years at a club perhaps even punching above their weight in fifth or sixth spot for a number of years. But it looks like he's taken them to another level, the passing game we all know is there, playing their way out from the back a little bit more. I've watched a few of their games and he's got them playing brilliantly but, as I said, that's no surprise because we know the way he works."