Their performance was encapsulated by a superb hat-trick by recalled centre Jonathan Joseph.
Joseph was dropped for the Italy game two weeks ago but marked his return with an impressive display.
Danny Care got two tries, Anthony Watson and Billy Vunipola one each and the peerless Owen Farrell kicked 26 points as England chalked up their highest score and joint-biggest win in 146 years of the oldest fixture in international rugby to retain the title with a game to spare.
England now have an unassailable lead on 18 points. Ireland and France, who gained a bonus point victory over Italy earlier, both have 10 points, then come Wales and Scotland on nine, with Italy last without a point.
England, whose previous highest score against the Scots was their 43-3 win in 2001, will now seek to complete back to back grand slams in Dublin next Saturday.
Today's victory was also England's 18th in a row, drawing them level with New Zealand, who set the tier one record from 2015-2016.
"We started well and our intensity was pretty good. It was the sort of performance we needed, said England coach Eddie Jones.
"Scotland were confident, they came down here with high expectations and we needed to play well.
"I was really pleased with our effort and now the focus is on the Grand Slam next weekend. The exciting thing is that we are only just starting. We are one year into a four-year project and we will only get better."
Scotland had not won at Twickenham for 34 years but arrived in good spirits with two wins under their belt having played some of their best rugby for many years.