The 75-year-old played for United between 1962 and 1973, winning two league titles with the club in 1965 and 1967 and the FA Cup in 1963 as one third of the club's 'Holy Trinity' alongside fellow stars Sir Bobby Charlton and the late George Best.
He was named European Footballer of the Year in 1964 but was ruled out by injury for the European Cup final in 1968, which United won by beating Benfica 4-1 at Wembley.
"We felt very fortunate to be playing football and to be getting paid," said when asked to recall what it was like to play in that great United side of the 1960s.
"We didn't get a great deal of money, but of course when I saw George Best come to the club as a young boy at 15, 16, I just looked at him and thought 'oh, this is going to be something special'
It doesn't always turn out that way, but it did with him and it was just lovely to play alongside him and enjoy the game."
Law admitted missing the 1968 European Cup final did still rankle with him, but was delighted to see United manager Sir Matt Busby triumph a decade on from the Munich air disaster in which eight of his players at the time were killed, with Busby and Charlton both suffering serious injuries
Law told BBC Radio Five Live: "The guys who went out and won the trophy for Sir Matt (Busby) were brilliant but I thought we would win it again because we had such a good team, but we got knocked out of the semi-final with AC Milan a year later
"But it was lovely for Sir Matt Busby to win that trophy when you think (it was) 10 years after the crash
For Matt to win the European Cup at Wembley was just wonderful for everybody."
Law has been in the news recently following an interview he gave regarding the current United side in which he was asked whether the team he played for in the 1960s would beat the 2015 edition
Law said they would beat the current team 1-0, and when asked why they would only win by such a narrow margin, Law joked: "Because we're all in our 70s now."
He remains a firm favourite at Old Trafford, and there is a statue of him at the Stretford End of the stadium, despite two spells with Manchester City either side of his 11-year stint with the Red Devils
In his second spell at City he scored a back-heeled goal against United as they were relegated from the top flight at the end of the 1973-74 season.
It proved to be Law's final touch in league football as he asked to be substituted immediately afterwards, and he later admitted: "I have seldom felt so depressed as I did that weekend."
Law began his career at Huddersfield before joining City for a British record transfer fee in 1960
He moved to Italian side Torino in 1961 and was then enticed back to Manchester by United boss Sir Matt Busby after struggling to adapt to life in Serie A.
In addition to his success at club level, Law also won 55 senior caps for Scotland, scoring a joint record 30 goals
Despite all his achievements with United he describes receiving his first senior Scotland call-up in 1958 as the greatest moment of his career.
In quotes published by the Sun in 2010 to mark his 70th birthday, Law said: "I was at Huddersfield Town at the time and was walking down the street.
"There was a bloke selling the local newspaper, the Huddersfield Examiner
Matter-of-factly, he told me I had been picked by Scotland.
"I could hardly believe it
It almost took my breath away
As far as I am concerned, there is no higher honour than representing your country
It would be fair to say I was absolutely overjoyed."
Law rounded off his career by representing Scotland at the 1974 World Cup in West Germany.
He scored 237 goals for United, and is joint second in the club's all-time scoring list behind his old team-mate Charlton after Wayne Rooney equalled Law's tally in November.
His CBE award is also in recognition for his charity work
Law has been a fund-raiser for Cancer Research UK and is a patron for the Meningitis Now charity, and successfully recovered from prostate cancer himself in 2003.
Source : PA
Source: PA