In his new autobiography, Life at the Limit, the 37-year-old - who was world champion in 2009 - describes Hamilton as "a brilliant, mercurial driver".

But he says the 32-year-old was "unpredictable" and he "regretted that despite our similarities, we were never really friends".

Button praises Hamilton for "really coming on over the past few years".

He added: "He's matured, become a bit of a statesman and a great representative of the sport."

Button, who retired at the end of last season but made a one-off return to Formula 1 at the Monaco Grand Prix this year, says he will never race again in F1.

He says the death in 2014 of his father, with whom he was very close and who accompanied him to nearly all his races, had taken the fun out of it.

"I've been offered drives in F1 but I'm not interested, although I will race in the future," Button says. "Just not F1. Not without dad."

A difficult relationship

Button describes three-time world champion Hamilton as "one of the greats", adding: "Of everybody on the grid, he's the guy who really has that 'gift'."

But he said their personal relationship was marked by tension throughout their three years as McLaren team-mates from 2010-12.

Button says he was warned by several people about joining McLaren because of Hamilton's talent and the way the team was perceived to be focused on him.

Button believes his arrival at McLaren with his entourage of close friends and his father changed the atmosphere, and that Hamilton feared it undermined his position with the team.

Describing their relationship early in their first season together, Button says: "Personally, he was fine with me, no issues at all at this stage of the game, but you could just tell he was a little bit peeved.

"That thing about it being his team? It was right on the money. And, if you ask me, he was finding it difficult to get a handle on the fact that it was our team now."

Button says that when he went to McLaren after winning the title with Brawn in 2009, he was "worried the atmosphere might be a bit lacking".

He adds: "So it was good that we were able to come in and lift the place, add a bit of much-needed levity.

"[But] I'm not sure that was to Lewis' taste. I don't think that I was to his taste, if I'm honest."

The two men have known each other since they were children - Hamilton's father bought an engine for his son's racing kart from Button's father when he was starting out.

And McLaren tried to build an impression that the two were great friends, conceiving a cartoon series in which each voiced their own character.

"[It] portrayed us as bantering rivals," Button says. "The rivalry was real... but there wasn't a great deal of banter."

He goes on to describe a series of flashpoints between them, including after the Turkish Grand Prix in 2010, when Hamilton believed Button had ignored team orders to pass him, and over some of Hamilton's controversial social media comments during his time at the team.

Button says: "As people, we had a lot in common. There was our shared karting history, not to mention the fact that his dad was a customer of my dad. And, unlike a lot of drivers in Formula 1, neither of us came from an especially wealthy background; we'd achieved what we had through talent and a lot of grafting.

"When we spent time together it was nice, and he'd always strike up a conversation with dad, and we'd hang out a bit. But at the same time there were an awful lot of awkward and uncomfortable silences, and often I'd think: 'What's going unsaid here?'"

He concludes he believes Hamilton has changed since then: "He's built on all that talent and hard work and he's a more rounded character as a result."

Comparing Hamilton and Alonso

In 2015 and 2016 Button was partnered at McLaren by Fernando Alonso, a driver held in similar admiration to Hamilton throughout F1.

"I'd say that over the years Fernando had been one of - if not the - toughest competitors I'd faced, both as a team-mate and a rival at other teams," Button writes.

"Lewis was unbelievably quick and could pull a lap out of the bag just like that; him and Ayrton Senna were the two quickest guys over one lap, maybe ever.

"But Fernando was the more rounded driver. I'd know, even if I out-qualified him, that he'd still be tough to beat in a race.

"He's nice on the outside, really affable and approachable, but beneath that he's a very, very tough competitor who'll do anything to beat you."